Question Video: Comparing Thinking and Braking Distances for Different Cars | Nagwa Question Video: Comparing Thinking and Braking Distances for Different Cars | Nagwa

Question Video: Comparing Thinking and Braking Distances for Different Cars Physics • First Year of Secondary School

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Data is being collected on two cars to test their safety. Below are two graphs that represent the two different cars. Each graph shows the thinking distance of each driver and the braking distance of each vehicle and how they change with different initial velocities. The safer car will slow down in a shorter time once a driver has applied the brakes. Which car is safer?

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Video Transcript

Data is being collected on two cars to test their safety. Below are two graphs that represent the two different cars. Each graph shows the thinking distance of each driver and the braking distance of each vehicle and how they change with different initial velocities. The safer car will slow down in a shorter time once a driver has applied the brakes. Which car is safer? (A) Car one is safer because it has a lower stopping distance at all velocities. (B) Car one is safer because it has a lower thinking distance at all velocities. (C) Car two is safer because it has a lower braking distance at all velocities.

In this question, we need to determine which of the two cars, car one or car two, is safer. This is the one that will slow down in a shorter time once the driver has applied the brakes.

To do this, let’s first recall that the thinking distance shown on each graph is simply the distance that the car travels while the driver is reacting to whatever it is that will cause them to brake. In other words, the thinking distances have nothing to do with which car is safer. They depend entirely on the driver and how fast the car was going before braking.

Let’s also recall that the braking distance of a car is the distance it travels once the brakes have been applied, until the car comes to a complete stop. This distance depends on various factors. One of these is the initial speed of the car. If the car was traveling very quickly before the brakes were pressed, it will travel a larger distance after the brakes have been pressed, until it comes to a complete stop, whereas a car moving very slowly will stop easily without traveling too far, once the brakes are applied.

Another factor affecting the braking distance of a car is the weather conditions in which the car is driving. If the road is wet or icy, the car will travel a larger distance once the brakes have been applied, because there is less grip with the road, as compared to if the weather is good and the road is dry.

In this question, we are comparing the braking distance of two different cars. So we can assume that both have been driven in the same conditions. This is the only way the comparison would be fair.

Yet, another factor that can affect the braking distance of the car is how strong or effective the brakes are and, more generally, how well the car is designed to be able to stop. With effective brakes, the car could slow down and stop much more rapidly once the brakes are applied, compared to a car with weaker brakes. And this is the factor that we are most concerned about here.

We want to work out which car is the safest, or best designed for braking. This will be the car that has a lower braking distance for any initial velocity. The reason for this is that the quicker a car can stop, the less likely it is to hit something in front of it, which is what the driver likely reacted to in the first place.

So to answer this question, all we need to do is to compare the braking distances of both cars for the same initial velocities. Starting with car one, we can see that if it was traveling at 30 kilometers per hour before the brakes were pressed, then the car will move a further 10 meters once the brakes are pressed before it fully stops. However, for the same initial velocity, 30 kilometers per hour, the second car will only travel six meters once the brakes are pressed before it fully stops. So for an initial velocity of 30 kilometers per hour, the second car has a better braking distance and is therefore safer.

We can conduct a similar sort of analysis for another initial velocity. For example, at an initial velocity of 65 kilometers per hour, car one has a braking distance of 20 meters, whereas car two has a braking distance of 17 meters for the same initial velocity. Once again, we see that car two is safer. In fact, for all the initial velocities shown on the graph, we see that car two is safer as it has the lower braking distance.

Looking back at our answer options, we see that option (C) most correctly describes what we have just figured out. Car two is safer because it has a lower braking distance at all velocities.

Quickly looking at the other answer options, we see that option (B) cannot be correct as it talks about thinking distance. And this is more to do with the driver of the car than the car itself. And option (A) talks about stopping distance, which we can recall is the sum of the thinking distance and braking distance. Again, this depends on the driver as well as the car itself so is not the best indicator of a car’s safety.

Hence, our final answer is option (C). Car two is safer because it has a lower braking distance at all velocities.

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