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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

A car is traveling at 50 mi/h when the brakes are fully applied, producing a constant deceleration of 22 ft/s2. What is the distance traveled before the car comes to a stop?

To determine

The distance travelled before the car comes to stop.

Explanation

Given data:

Travelling velocity of car 50mih and deceleration is 22fts2.

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:

The initial displacement is zero, that is s(0)=0. The initial velocity is 50mih, that is,

v(0)=50mih=50(52803600)fts{1mih=52803600fts}=2203fts

Acceleration is indicated by adding a negative sign to Deceleration.

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

a(t)=22

Substitute –22 for a(t) in equation (1),

v(t)=22

Antiderivate the expression with respect to t.

v(t)=22t+C (3)

Here,

C is arbitrary constant.

Substitute 0 for t in equations (3),

v(0)=22(0)+C=C

Substitute 2203 for v(0),

C=2203

Substitute 2203 for C in equation (3),

v(t)=22t+2203 (4)

Substitute 22t+2203 for v(t) in equation (2),

s(t)=22t+2203

Antiderivate the expression with respect to t

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