Q31.

Expert-verified
Found in: Page 44

### Physics Principles with Applications

Book edition 7th
Author(s) Douglas C. Giancoli
Pages 978 pages
ISBN 978-0321625922

# Determine the stopping distance for an automobile going at a constant initial speed of 95 km/h and a human reaction time of 0.40 s (a) for acceleration and (b) for .

(a) The stopping distance is 126.63 m when the acceleration is .

(b) The stopping distance is 68.60 m when the acceleration is .

See the step by step solution

## Step 1. Relation between initial velocity, final velocity, acceleration, and displacement

The acceleration of an object is defined as the rate at which the velocity of the object changes in a given amount of time.

Given data.

The initial speed of the car is .

The final speed of the car is as it comes to a stop.

Now,

Rule.

If during the deceleration of the car, the traveled distance is ,

Then,

.

## Step 2. Calculation of the traveled distance before applying the brakes due to the reaction time

Here, the car moves at the same speed during the reaction time before applying the brakes.

The reaction time is .

Therefore, due to the reaction time, the car travels a distance of before the application of the brakes.

Now,

## Step 3. Calculation of the stopping distance for the acceleration

(a) When the acceleration is , from equation (i),

Therefore, the stopping distance is 126.63 m when the acceleration is .

## Step 4. Calculation of the stopping distance for the acceleration

(b) When the acceleration is , from equation (i),

Therefore, the stopping distance is 68.60 m when the acceleration is .