Question Video: Identifying the Correct Velocity-Time Graph for a Stopping Vehicle | Nagwa Question Video: Identifying the Correct Velocity-Time Graph for a Stopping Vehicle | Nagwa

# Question Video: Identifying the Correct Velocity-Time Graph for a Stopping Vehicle Physics • First Year of Secondary School

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The velocity–time graph shows the change in the velocity of a car that suddenly brakes to come to a stop on a dry concrete surface. Which of the other graph shown, (a), (b), (c), (d), and (e), best matches the velocity–time graph for the same car stopping, driven by the same driver, but where the car travels on a wet concrete surface?

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### Video Transcript

The velocity–time graph shows the change in the velocity of a car that suddenly brakes to come to a stop on a dry concrete surface. Which of the other graph shown, (a), (b), (c), (d), and (e), best matches the velocity–time graph for the same car stopping, driven by the same driver, but where the car travels on a wet concrete surface?

In our first graph, we see the velocity of a car plotted against time. We’re told that this corresponds to the velocity over time of a car that brakes and then comes to rest on a dry concrete surface. We can see that at first the velocity of the car is constant. The interval of time over which this occurs corresponds to the driver’s reaction time. At the end of the driver’s reaction time, the driver will press down on the brake pedal, and the car begins to decelerate with its velocity decreasing until it reaches zero. We want to compare this graph, which corresponds to the car coming to a stop on a dry concrete surface, with the other five graphs given to us as answer options. We’re told that these options are meant to represent the same exact scenario, except that this time the car is coming to a stop on a wet concrete surface.

In other words, we’re working with the same car, with the same initial speed, with the same driver, with the same reaction time, and so on. Knowing this, we can start to look over graphs (a), (b), (c), (d), and (e) and even begin eliminating some of the options that won’t fit. For example, notice that the length of the horizontal segment of this line in graphs (a), (b), and (d) is longer than it is in our original graph. If this were accurate, it would mean the driver of the car now has a slower reaction time, but that’s not true. The only difference between these two scenarios is that in the first case the concrete is dry, and in the second case it’s a wet surface. This means that right away we can eliminate answer options (a), (b), and (d) from consideration.

Looking back at our original graph, we see that the initial speed of the car is measured to this point on the vertical axis. When our car drives on a wet concrete surface, we expect this initial speed to be the same. Looking at answer choice (e), we see that here the initial speed of the car, the horizontal line segment on this graph, is greater than it is in our original graph. This would mean that the car is moving faster at first on the wet concrete surface than on the dry. This though goes against the fact that we’re working with the same car in both cases. We’ll cross off answer option (e) as well.

That leaves us with just one remaining option. Let’s test if this option is correct. First, we can see that the reaction time of the driver in this case is the same as it was in our original graph. We also see that the initial speed of the car in this case is the same as before. But we can see that the difference in time between the point where the driver begins to apply the brake and the point where the car comes to a stop is greater for graph (c) than it is in our original velocity–time graph. This means that graph (c) is showing us a slower deceleration of the car compared to our original graph.

That though makes sense because the surface the car is driving on now is wet with less friction than the dry concrete surface. We would expect then for the car to decelerate more slowly, that is, to take more time to come to a complete stop. This is just what graph (c) shows us. And so we choose this graph as our answer. This graph best matches the velocity–time graph we would expect of a car that could generate this velocity–time graph but that is now driving on a surface with lower friction.

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