   Chapter 4.9, Problem 76E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# A car braked with a constant deceleration of 16 ft/s2, producing skid marks measuring 200 ft before coming to a stop. How fast was the car traveling when the brakes were first applied?

To determine

The velocity of car when brakes were applied.

Explanation

Given data:

Deceleration is 16fts2 and displacement is 200 ft.

Formula Used:

Write the expression for acceleration function a(t) .

a(t)=v(t) (1)

Here,

v(t) is first derivative of velocity function v(t) .

Write the expression for velocity function v(t) .

v(t)=s(t) (2)

Here,

s(t) is first derivative of displacement function s(t) .

Antiderivative of tn is tn+1n+1 and 1 is t.

Calculation:

Consider the initial velocity of car as v0 and the initial displacement is zero, that is s(0)=0 .

Acceleration is indicated by adding a negative sign to Deceleration.

Write the expression for acceleration (a(t)) .

a(t)=16

Substitute –16 for a(t) in equation (1),

v(t)=16

Antiderivate the expression with respect to t.

v(t)=16t+C (3)

Here, C is arbitrary constant.

Substitute 0 for t in equations (3),

v(0)=16(0)+C=C

Substitute v0 for v(0) ,

C=v0

Substitute v0 for C in equation (3),

v(t)=16t+v0 (4)

Substitute 16t+v0 for v(t) in equation (2),

s(t)=16t+v0

Antiderivate the expression with respect to t.

s(t)=16(12t2)+v0t+D

s(t)=8t2+v0t+D (5)

Here,

D is arbitrary constant

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