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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
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

To find:

The speed of car when the brakes are applied.

Explanation

1) Concept:

If F is an antiderivative of  f on an interval I, then the most general antiderivative of f on I is Fx+c, where c is an arbitrary constant.

2) Given:

Constant acceleration is

 αt=-16ft/s2

3) Calculations:

We have the constant acceleration αt=-16ft/s2, where a is a constant.

Taking the general antiderivative of αt,

vt=-16t+v0, where v0 is the speed of car when brakes are applied.

The car stops when, vt=-16t+v0=0

 t=116v0

Now taking the general antiderivative of  vt

st=-16t22+v0t+s0 Here, s0=0, because car was stopped

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