Basic concepts such as displacement velocity acceleration projectile |

So let's begin the first thing we're going to talk about is distance and displacement now many of you out there are very familiar with the word distance when you think of distance when you hear the word distance what do you think of I think of how far something has traveled so let's say the distance between one city to another could be a hundred miles and so is the difference between two points now displacement is very similar to distance but displacement encompasses direction as well direction is important for displacement so let me give an example that distinguishes distance and displacement

So let's say if you have a person let's say John and he's at this position right here and he decides to walk let's say eight meters east and then he turns any other direction and travels let's say three meters west the total distance that John travels is eight plus three or eleven meters however his displacement is not eleven but rather his displacement is five meters displacement is the difference between the final position and the initial position so let's say if we have a number line and let's say this is position zero so John traveled eight meters east

So now he's at position eight on a number line so during the first part of his trip his displacement was positive eight then he traveled three meters Wes so his displacement is negative three so now he's at position 5 and so his net displacement is five meters because he started from position a and now he's at position B which is located at position 5 and so your net displacement is basically it's the final position let's say PF minus the initial position his final position is position five his initial position is zero so his displacement is positive five he went from A to B and so that's the basic idea behind displacement the total distance is.

11 now distance is a scalar quantity it only has a magnitude displacement is a vector quantity it has both magnitude and direction in the case of distance in the first part of the trip he traveled a distance of positive 8 in the second part he traveled a distance of positive 3 and so the total distance is 11 meters now displacement has a magnitude and direction during the first part of his trip his displacement was positive 8 the magnitude is how far he traveled which is 8 meters the direction is he's traveling east and so we have a pause sign for going in the eastward direction anytime you go towards the right you going in the.

Positive x-direction so the displacement is positive now during the second part of the trip he's traveling west that is towards the negative x-direction and so it's negative 3 in terms of displacement but in terms of distance it's positive 3 keep this in mind distance is always positive but displacement can be positive or negative if you're traveling east or north the displacement has a positive value if you're traveling west or south displacement has a negative value and so if you add up the displacement for the first part of the trip plus the displacement of the second part you get the net displacement of positive 5 positive 8 plus negative 3 will give you positive 5 now let's say a car travels 200 miles would this description be related to distance or displacement so if I say you traveled 200 miles am I describing distance or displacement well this would be a description of distance because no direction was indicated.

So you could be going east-west north or south if you simply state 200 miles you're describing distance now let's say if the car traveled 300 miles north, in this case, I have the magnitude which is 300 miles and I also have the direction which is in Norfolk direction so in this case I'm describing displacement is a vector quantity it has both magnitude and direction whereas a distance is a scalar quantity it only has magnitude such as 200 miles without any direction so make sure you understand the difference between a scalar.

Quantity and the vector quantity a scalar quantity as we said before has magnitude only but a vector quantity has a magnitude and direction now let's talk about speed when you think of the word speed what do you think of speed tells you how fast something is moving so let's say if a car is traveling 30 meters per second what does that mean so that means that every second the car will have traveled a distance of 30 meters so let's say this is the starting line and I'm going to use a box to represent a car and the car is moving in this direction with a speed of 30 meters

Per second so one second later the car will have traveled a total distance of 30 meters two seconds later is going to travel another distance of 30 meters so for a total distance of 60 meters so we could make a table so let's put T for time D for distance so if the speed is 30 meters per second so every second the distance traveled will increase by 30 and so that's what speed tells us it tells us how fast a distance of an object or the distance traveled by an object is changing every second so let's say if you're driving a car and you're going 60 miles.

Per hour every hour at that speed, you will travel a distance of 60 miles so let's say if you want to travel a distance of 300 miles it's gonna take you five hours to do so in the first hour you're gonna travel 60 miles in a second hour you have covered a distance of 120 miles so every hour you're gonna travel an additional distance of 60 miles now there's a formula that you need to know and it's D is equal to V T in this equation D can be used as distance and V represents speed T represents time now sometimes with this formula you could use the velocity in terms of.

V and if you do so then D will no longer technically be represented by distance but it's going to be represented by displacement and so you could use that simple formula in many different ways so here's a question for you so let's say if you have an object that is moving at a speed of let's say 50 meters per second how long will it take for this object to travel a distance of 1000 meters so we're looking for the time how long so we could use this formula D is equal to VT so the distance is a thousand meters the.

V is 15 meters per second that we'll need to calculate the time so we can divide both sides by 50 and so it's going to be a thousand divided by 50 and if we cancel a zero that's a hundred divided by five which is 20 so it's gonna take 20 seconds for this object to travel a distance of a thousand meters now let's talk about speed and velocity so what is the difference between these two quantities because they both describe how fast something is moving but there's a difference between them speed is a scalar quantity and velocity is a vector quantity speed is always positive velocity can be positive or negative now recall that a scalar quantity only has magnitude whereas a vector quantity has magnitude and direction so can you think of some.

Examples that will distinguish speed from velocity so let's say if a train I'm going to use a box again is moving at 45 meters per second let me take away the arrow so I you don't have any direction it's simply moving at 45 meters per second, in this case, this describes the speed of the train because I'm telling you how fast it's moving but not where it's going now let's say if we have a train moving at 30 minutes per second going west, in this case, this is a description of velocity because not only do you have the magnitude of the vector which is the speed but you also have the direction and so when you combine magnitude and direction you have a vector quantity and so velocity is basically sped with direction the 30 meters per second tells you the.

speed was telling you the direction and when you combine these two you have velocity so let's summarize a few key points speed tells you how fast something is moving velocity tells you not only how fast something is moving but also where it is going so remember velocity is speed with direction speed can only be positive velocity can be positive or negative so if V is negative 20 meters per second you know you're dealing with velocity because it's negative if you're looking for the speed the speed would be positive 20 meters per second.

Speed is always positive and you could say the speed is the absolute value of velocity can be positive or negative but speed is always positive so if the velocity was negative 35 m/s the speed is automatically positive 35 m/s now there are some mathematical formulas that you want to know when dealing with speed and velocity there's something called average speed because sometimes in physics you need to calculate the average speed of an object the average speed can be calculated by taking the total distance traveled by the object and dividing it by the total time now if you think about this formula D is equal to.

VT V can be described as the speed or the velocity so if you divide both sides by T you could cancel this on the right side you'll see that V which is the average speed, in this case, is equal to D over T so average speed V is equal to the total distance D divided by the total time T now what about average velocity let's say if we wish to calculate average velocity how can we do so average velocity is equal to displacement divided by the total time so in this case the formula looks the same average velocity can be represented by V displacement can be represented by D and the time is T so the formula looks identical but the meaning is different so keep this in mind velocity is associated with displacement speed is associated with a distance now let's say if you have an object and its object traveled twelve meters east and then it travels.

20 meters west and it did so in a time period a total time period of four seconds so let's say going from position a to position B that's a distance of 12 meters and from position B it's a position C 20 meters so that total trip from A to C took only 4 seconds so for this object going from A to C what is the average speed of the object and also what is the average velocity so to calculate the average speed we need to determine the total distance and divided by the total time the total distance is simply 12 plus 20 if you add those two numbers it will give you 32 meters and the total time is 4 seconds so 32 divided by 4 is 8 so the average.

speed is positive 8 keep in mind speed is always positive now what about the average velocity well we know that average velocity is defined as displacement divided by the total time the displacement for the first part of the trip going from A to B is positive 12 because the object is traveling in a positive x-direction the object is going east for the second part of the trip the object is traveling west towards the negative x-direction and so going from B to C the displacement is negative so if we add up 12 and negative 20 we can get the net displacement which is negative 8 now keep in mind you can also treat this as a number line let's say a is our position zero B will be at position 12 and then if you do 12 minus 20 you'll see that.

C is a position negative 8 and the difference between these two positions will be the net displacement which is still negative 8 so the final position minus the initial position will give you the net displacement now let's divide it by 4 seconds so the average velocity is negative 2 meters per second and it makes sense because the net result is that the person traveled in the in a westward direction towards the negative x-axis so going from A to C ignoring be the person traveled towards the west and that's why the velocity is negative because any time you go in in the west direction towards the negative x-axis it will be negative if you're going towards the positive x-axis or in the eastward direction it's going to be positive the video that you're currently watching is the first half of the entire video now in the second half I do talk about.

Newton's third law a mass versus weight static friction kinetic friction and even some things that you don't see here like the normal force and how you can increase it and decrease it how you can increase and decrease friction the centripetal force centripetal acceleration and gravity kinetic energy potential energy elastic potential energy work momentum and elastic collisions and some other things as well to include an impulse so those are a few things that I'm going to talk about in the second half of this video and you can access it on my patreon page if you wish to support it so that's it and now let's move on to our next.

Topic now let's talk about acceleration what is acceleration now you've encountered acceleration when driving a car a good way to think about it is imagine two vehicles let's say a truck I'm not the most artistic person but we'll work of this and let's say a sports car which of these two vehicles have let's say a greater acceleration is it the truck or the sports car so what is acceleration tells you how fast the speed is changing or more technically how fast the velocity is changing so the truck can probably go from 0 to 60 miles in maybe let's say 30 seconds a sports car can go from 0 to 60 in a shorter period of time let's say in five seconds

So because the sports car can get to a higher speed or to a certain speed faster than a truck it has a greater acceleration and so acceleration tells you how fast the velocity is changing acceleration is defined as the change in velocity divided by the change in time or sometimes you could just put T so you can write it this way let me adjust the formula so if you see the triangle it simply means change so acceleration can be written this way it's the final velocity minus the initial velocity divided by the time so to calculate the acceleration of the truck noticed that the change in velocity is 60 60 minus zero is 60 divided by the time which is 30

So 60 divided by 30 is 2 so the acceleration of this truck is 2 miles per hour per second because we divided miles per hour by second so it's miles per hour per second now the acceleration of the sports car is 60 miles per hour that are the change in velocity divided by 5 seconds 60 divided by 5 is 12 so it's 12 miles per hour per second as you can see the acceleration of the sports car it's much greater than the acceleration of the truck is going to take a long time to go from zero to 60 but the sports car will get there a lot faster and so it has a greater acceleration and so that's the basic idea behind acceleration it tells you how fast the velocity is changing now let's make a table let's say if an object is moving with an initial speed of 12 meters per second

So vo tells you initial speed or initial velocity now since I have an arrow let's say it's going east this now is it becomes the description of velocity if I put direction with it and let's say at this point this object or vehicle begins to accelerate at a rate of 4 meters per second square so this is 4 meters per second per second so what does that mean so if we make a table if we plot time and velocity let's say the final velocity at a certain time at T equals zero this becomes the initial velocity so it's 12 what would the velocity be 1 second later well the acceleration tells us how fast the velocity is changing so because the acceleration is positive for that.

Means that the velocity is increasing by 4 meters per second every second so anytime acceleration is positive the velocity is increasing anytime the acceleration is negative the velocity is decreasing so one second later the velocity will now be 16 2 seconds later the velocity is 23 seconds later it's 24 4 seconds later it's 28 and so every second the velocity will increase by 4 meters per second because the acceleration is 4 meters per second per second now the formula that you want to use to calculate final velocity is this equation the final is equal to.

V initial plus 80 now let's say we have another object that is moving in an eastward direction at a speed of let's say 24 meters per second but this time let's say the acceleration is negative 6 meters per second square what's going on here is this object speeding up or slowing down whenever the acceleration and velocity whenever they have opposite signs the object is slowing down whenever they have the same sign it's beaten up in the last example the acceleration was positive 4 and the velocity had positive values it started with positive 12 and so because the velocity and acceleration had the same sign the object was speeding up

So you may want to write this down the object will be speed enough that is the speed will be increase in if acceleration and velocity have the same science if they're both positive or if they're both negative the object will be slowing down if the acceleration and velocity have opposite signs either positive a negative or negative and positive and this example will illustrate that so this time we're gonna make a table with time velocity and I'm going to use s for speed or SP for speed so at T equals zero the velocity is positive 24 and remember speed is the absolute value of velocity so the speed is positive 24 now one second later what will be the new velocity well the acceleration is negative six and we call that if acceleration is negative the velocity will be decreasing so it's going to decrease by six so 24 minus six is 18 two seconds later it will be.

12 three seconds later it's gonna be six-four seconds later it's ceará five seconds later it's negative six and then so forth now speed is always positive it's the absolute value of velocity so here the speed is positive 18 positive twelve positive six zero positive six positive 12 and so forth now let's focus on the first half in the first four seconds the object is slowing down if you look at the speed is decreasing from 24 to zero so what's happening is that the object is moving but over time it's moving slower and slower and slower and.

so at four seconds I that instant is not moving whether it's changing direction notice the velocity it's going from positive to negative which means that is changing from an eastward direction to a westward direction and it begins to move faster towards the west so as you can see it speed enough because the speed is increasing after four seconds now remember what we said before if acceleration and velocity if they share the same sign then the object will be speed enough that is if they're both positive or both negative but if they have opposite signs then the object is slowing down so during the first four seconds the velocity is positive and the acceleration is always negative therefore because the signs are opposite it's.

Slowing down the speed is decreasing from 24 to zero now during the second part of this problem that is after four seconds the velocity is negative and the acceleration is negative so because they share the same sign the object is speeding up as you can see the speed increases from zero it's a positive 18 in the next three seconds so make sure you understand that concept if acceleration and velocity share the same sign the object is speeding up if they have opposite signs it's slowing down now let's move on to gravitational acceleration in physics you'll see this symbol that looks like a G and it's equal to negative 9.8 meters per second squared so this is the gravitational acceleration of planet Earth and it varies for different planets and other very large objects so the gravitational acceleration of the moon, for example, is negative.

1.6 meters per second squared it's a lot less for one reason the moon has less mass than the earth and so you will weigh a lot less on the moon you'll feel lighter on the moon and so you can jump higher on the moon but let's focus on the gravitational acceleration of the earth negative 9.8 what does that mean well in the last example we saw what a negative acceleration can do to velocity and so the fact that this gravitational acceleration is negative means that it will always decrease the velocity now the gravitational acceleration of the earth it acts in the Y direction and not in the X direction and so let's talk about velocity is a vector and it can have an.

X component and it can have a Y component the actual velocity is basically the hypotenuse of this right triangle VX is the horizontal component of this velocity vector V Y is the vertical component the gravitational acceleration does not affect VX it affects the V Y so technically you can write this as G Y it's a vertical gravitational acceleration it doesn't affect the horizontal velocity it affects the vertical velocity to make sure you understand that now let's use an example to help us understand G Y sometimes it can be written as a Y.

So a Y and G are basically the same it's negative 9.8 let's say we have a person who was standing on top of a cliff next to the ocean and this person has a ball in his hand and he released the ball from rest so he doesn't throw it down and throw it up he simply lets go of the ball well we know what's gonna happen gravity's gonna cause the ball to fall now what can you tell me about V why the vertical velocity of the ball over time will it become positive or negative well know that velocity is speed with direction and right now the ball is going to be moving in the negative y-direction so this is positive x this is negative x positive Y negative.

Y it's going down in the negative y-direction so V Y will become negative if we make a table with T and V Y at T equals zero the initial vertical velocity will be zero because the ball was released from rest now the acceleration or also called acceleration due to gravity is negative 9.8 because it's negative the vertical velocity will be decreasing so every second it's going to decrease by 9.8 so two seconds later it's going to be negative nineteen

Point six three seconds later it's negative twenty-nine point four now the speed is always going to be positive so if you are asked what is the speed of the ball let's say three seconds later it's going to be positive twenty-nine point four meters per second but if a test question asks you for let's say the velocity of the ball three seconds later you should say it's a negative twenty-nine point four meters per second because it's going in the negative y-direction and so hopefully this number makes more sense so the gravitational acceleration tells you how fast the vertical velocity is changing every second so on the moon where a.

G is negative 1.6 if you were to drop a ball the vertical velocity will decrease by 1.6 and meters per second every second so let's say we have a similar situation we have the same person with the ball in his hand and this time he throws it in the upward direction with an initial speed of twenty-nine point four meters per second what can you tell me about the vertical velocity and its values every second let's say this person is still on the earth where.

G is negative 9.8 meters per second squared so even though right now the velocity is positive because she is negative the vertical velocity will decrease so as the ball goes upward its slowing down because the velocity is positive and the acceleration is negative because they're opposite in sign the ball is slowing down eventually the ball will reach its maximum height and then it's going to change direction and begin to fall down so if we make a table between.

T and V Y we're gonna get the following values so at T equals zero that is initially the vertical velocity is positive twenty-nine point four now the acceleration tells us how fast or how much the velocity changes every second so one second later it's going to decrease by 9.8 so twenty nine point four minus nine twenty-eight will give us nineteen points six so one second later it's going to be positive nineteen point six two seconds later we'll need to decrease this again by nine-point eight so it's going to be positive nine point eight three seconds later it's gonna be at zero so when the vertical velocity is at zero that means that it's no longer going up anymore and it's not going down yet it has reached its maximum height.

So it took three seconds to get to its maximum height so let's call this position a position B and position C so once he is zero it's a position a when C is three is that position B four seconds later it's going to be negative nine point eight five seconds later negative nineteen points six seconds later negative twenty-nine point four and so forth and.

So once it gets to position B once it passes that position the velocity will be negative because it's now going in the downward direction or in the negative y-direction so that's the mathematical profile of this situation so now you understand what's happening to the velocity values as time progresses so anytime the acceleration is negative the velocity is decreasing as you can see it started with a positive value and now it's becoming negative now the next topic that you want to be familiar with is something called projectile motion so what is a projectile is basically an object that is moving under the influence of gravity.

So in the last two examples the ball that was a release from rests and the ball that was thrown upward were behaving as projectiles because once release they were under the influence of gravity and in a typical physics course when dealing with projectile motion Frick is usually ignored and so we're not going to talk about it here so far we've considered one-dimensional projectile motion that is in the y-direction the first case was a ball going straight down the second case was the ball going up and then down so it's one-dimensional because it's only one direction, in this case, the y-direction but let's talk about projectile motion in two dimensions that is in the.

X and in the Y direction so one example that you'll see is a ball being kicked off a cliff or rolling off a cliff initially it's moving in the X direction and then it falls down like this and so the path that the ball travels is known as the trajectory hopefully I said that right the trajectory but now let's see the ball was kicked off the cliff at a speed of let's say five meters per second so what can you tell me about the vertical and horizontal components of the velocity of the ball at different times so let's make a table between T VX and V Y so initially at once he is 0.

VX is positive 5 because at that instant it's moving only in a horizontal direction so if you look at the trajectory this line is only going to the right it's not going up or down it's just going to the right now the vertical velocity is zero because it's not it doesn't have any component in the Y direction now one second later let's say the ball is over here so now the ball is moving in this direction so the velocity can be broken up into its X component so it's still moving to the right and the Y component it's moving down so let's call this point a and that point B so at point B because it's going in this direction it has a VX value and a V Y value and let's say point.

B is one second later from point eight so point eighty is zero and that point B T is one so what is the velocity at point B and what is the velocity at Point C let's see and what T is two seconds one second later we know what V y is going to be due to gravitational acceleration the vertical velocity will decrease by 9.8 every second so two seconds later it will be negative nineteen point six three seconds later negative twenty-nine point four now what about.

VX now it's important to understand that G negative nine-point a is a vertical acceleration not a horizontal acceleration it's not a y I mean it's not an X but it's a Y so this number does not affect a VX so when dealing with projectile motion unless this ball have some rocket thrusters VX is constant it doesn't change so for projectile motion the acceleration in the horizontal direction is zero so unless there's some kind of force that's propelling the ball to the right that is after it's been kicked ax is zero so it's important to keep that in mind and if ax is zero that means that.

VX does not change if the acceleration is zero the velocity is not changing the velocity is constant so to summarize what we've learned here when dealing with projectile motion it's important to understand that the velocity in the X Direction V X is constant it doesn't change unless the problem states that there's something accelerating it in a horizontal direction if there's no specific statement as such a tax is zero and V axis constant but for any projectile motion problem.

V, why it changes V y, is gonna change by 9.8 every second here is another projectile motion situation let me start at the bottom so let's say we have a ball and the ball is kicked off the ground at an angle it goes up and then it goes down now typically you might be given the velocity that which is kicked let's say it's going up at a speed of 40 meters per second and let's say it's at an angle of 30 so you have V which is 40 and you have the angle theta which is 30 degrees now what you need to do is find VX and V Y V ax is basically V cosine theta and this is the initial value.

V Y is V sine theta now for this problem I'm gonna give you VX and V Y so we're gonna choose some different values but in a typical problem when you're given V and theta you can find VX and V Y using those formulas but let's say that you discover initially the VX is let's use a nice number 8 m/s and V Y we're gonna say is 29. 4 meters per second so that's at a time value of zero what's gonna happen one second.

Basic concepts such as displacement velocity acceleration projectile motion Newton's
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December 21, 2019
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