WEBVTT physics/ap-physics-1-2/fullerton
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Hi everyone and welcome back to Educator.com.
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In this mini-lesson, we are going to go over the APlusPhysics worksheet on kinematics graphing motion and you can download that worksheet at the link below.
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Let us dive right in.
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Number 1 -- A cart travels with a constant non-zero acceleration, so we have some amount of acceleration or a change in speed, a change in velocity along a straight line.
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Which graph best represents the relationship between the distance the cart travels and the time of travel?
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We are being given here distance time graphs and we want the one that shows a constant non-zero acceleration.
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Well, if you recall, the way you get velocity from a distance time graph is to take the slope.
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If I start over here, I start with a very low slope and I go to a high slope.
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That means we must have a change in velocity.
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A velocity graph would probably look something like that if it were a velocity time graph.
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Here we have a negative constant slope, so we would have a negative velocity.
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Here we start out with a positive slope, so we would start up here for velocity, where we have a 0 slope and over here it is negative, so we would probably have a velocity time graph that looked like that.
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Over on the right, we have a constant positive slope, so we would have a constant positive velocity, but we want the one with a non-zero acceleration and it has to be constant.
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Up here we have a change in velocity, but at a constant rate and the slope of this would give us the acceleration, which would be positive in constant, so purple, if that is our acceleration time graph, is a constant value and it is non-zero, so our correct answer must be 1.
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Or as you look at this, you can think about it from the graph that you have a change in distance over time and the rate at which your distance is changing is increasing and it is increasing at a constant rate.
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You can use that to solve it too. Regardless, the best answer there is Number 1.
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Number 2 -- We have a car on a straight road that starts from rest and accelerates at 1 m/s² for 10 s, then the car continues to travel at constant speed for an additional 20 s.
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Find the speed of the car at the end of the first 10 s.
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Well, what we know when it starts out is it starts from rest, so our initial velocity is 0 and it accelerates at 1 m/s² for a time of 10 s.
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For the first 10 s, we want to know the speed at the end of that first 10 s.
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Well, final velocity equals initial velocity plus acceleration times time, so that is going to be 0 + 1 m/s² (acceleration) × 10 s (time)...
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...which implies then that our velocity is going to be 1 m/s² × 10 s is just going to be 10 m/s.
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The speed of the car at the end of the first 10 s is 10 m/s.
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Continuing on with the same story, a car on a straight road has the same story, but on the grid below, we are going to use a ruler to construct a graph of the cars speed as a function of time for the entire 30 s interval.
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At the end of 10 s, we know that our car was going 10 m/s, so I can draw that on my graph and then it continues to travel at constant speed for an additional 20 s, so that would be our graph of speed versus time.
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Number 4 says calculate the distance the car travels in that first 10 s and there are a couple of ways we could do that.
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You could take the graph and you could take the area under the graph or you could use your kinematics.
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Since we are talking about motion graphs, let us take the area under the graph in that first 10 s of the graph.
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And the shape there is that of a triangle, so we had 10 s here, we had a maximum speed of 10 m/s, so the area then of our triangle, which will give us the distance traveled...
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...The area of a triangle is 1/2base × height, so that will be 1/2 × 10 s × 10 m/s or 50 m and you could have also have done that with kinematic equations as well.
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Number 5 -- A student throws a baseball vertically upward and then catches it when it comes back down.
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If we consider vertically upward the positive direction -- so up is positive (y) -- which graph represents the relationship between velocity and time for the baseball, neglecting friction?
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When I throw it up, the moment it leaves my hand, it has a large positive velocity and as it goes further and further up, it slows down, slows down, slows down and at its highest point it stops, so part way through its path it is going to have 0 velocity and then it is going to come back down.
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It has a greater and greater magnitude, greater and greater speed, but in the opposite direction, so it is going to have a larger and larger negative velocity.
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The graph that shows this best is Number 4.
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We could also take a look at this graph and say if we wanted to know the acceleration, what would the acceleration look like?
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The acceleration is going to be the slope of that line, which the slope of that line is negative and constant, so our acceleration time graph would be down here at negative.
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That is actually going to be -9.8 m/s² as the acceleration due to gravity.
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What would that negative mean? Well, if we called up the positive direction, the acceleration due to gravity is in the opposite direction down, so that negative is indicating the direction there.
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Let us take a look at one more. The graph below represents the displacement of an object moving in a straight line as a function of time.
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What was the total distance traveled by the object during this 10 s interval?
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Let us take a look and see what we can figure out.
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As we start here at (0,0) and we go up through that distance, we have traveled 8 m .
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Then we have no change in displacement there and the next 2 s, we travel from 8 to 16 m, so we travel another 8 m.
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Then, finally, we come back another 8 m, but because it is distance traveled, that is the total amount of distance you are covering, so we have to add that in.
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Our total would be 24 m and our best answer there is Number 4.
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That finishes page 1 of the worksheet.
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Thanks so much and make it a great day everyone!