When a driver brings a car to a stop by braking as hard as...

When a driver brings a car to a stop by braking as hard as possible, the stopping distance can be regarded as the sum of a "reaction distance," which is initial speed multiplied by the driver's reaction time, and a "braking distance," which is the distance traveled during braking. The following table gives typical values. (a) What reaction time is the driver assumed to have? (b) What is the car's stopping distance if the initial speed is $25 \mathrm{~m} / \mathrm{s} ?$

Key Concepts

Kinematics of Deceleration

The kinematics of deceleration involves the study of motion under a constant negative acceleration. In the context of braking, it provides the equations needed to relate initial speed, deceleration, and the distance covered during braking. This analytical framework is crucial in understanding how vehicles slow down over a given distance once the brakes are engaged.

Stopping Distance

Stopping distance is the total distance a vehicle covers from the moment a driver perceives a situation requiring a stop to the moment the vehicle finally comes to rest. It is the sum of the reaction distance and the braking distance, underscoring the combined effects of human response and vehicle dynamics in everyday driving scenarios.

Reaction Distance

Reaction distance is the distance the vehicle travels during the driver’s reaction time. It is computed by multiplying the vehicle's initial speed by the reaction time. This concept illustrates how human response delays can contribute to the overall stopping distance of a vehicle.

Braking Distance

Braking distance is the distance a vehicle travels from the moment brakes are applied until it comes to a complete stop. This distance is determined by the vehicle’s initial speed and the rate of deceleration due to braking. Understanding braking distance is essential in analyzing vehicle stopping performance under uniform deceleration conditions.

Reaction Time

Reaction time is the interval between the moment a driver perceives a hazard and the moment the driver begins to respond, such as applying the brakes. It is a critical period during which the vehicle continues to travel at its initial speed, and its value directly affects the distance covered before any deceleration begins.

Transcript

00:02 So in this question, we are looking at the stopping distance of a car, as well as the reaction distance of a person breaking in the car as well.

00:15 So the first part wants to know what reaction time is assumed for the driver.

00:22 So we have three values for the initial speed and the reaction distance.

00:26 So we're going to assume that the driver is moving at constant velocity during the time that they are covering this reaction distance.

00:32 So we can use the equation v equals d over t.

00:36 Now any three or any of the three rows in our data table there will work to figure out the reaction time.

00:45 I'm going to use the first row.

00:47 So we have our 10 meters per second to the driver's moving.

00:52 They cover a distance of 7 .5 meters before they begin to break over t.

01:02 Multiply t to both sides, divide by 10.

01:05 So we got a reaction time at 0 .75 seconds.

01:13 And again, you can try this with any of the three rows.

01:15 It will give you the same value.

01:18 So now we want to know what is the braking distance, sorry, the overall stopping distance of the car was moving at 25 meters per second.

01:27 So this time we're taking the braking distance value to figure out our acceleration.

01:35 That's what we have to do first.

01:36 So i'm going to take our first row again, so we know that the initial velocity of the car is 10 meters per second.

01:49 We know that the distance that the car is going to break in is 5 meters.

01:56 We know the final velocity, not question mark, we know the final velocity is zero because they're stopping.

02:05 So the equation that we're going to use here is one of the kinematic equations...

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