   Chapter 3.9, Problem 71E

Chapter
Section
Textbook Problem

# A car is traveling at 100 km/h when the driver sees an accident 80 m ahead and slams on the brakes. What constant deceleration is required to stop the car in time to avoid a pileup?

To determine

To find:

The constant acceleration to stop the car in time to avoid a pileup.

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:

vt=100 km/h

3) Calculations:

Assume that αt=k km/h is the constant acceleration.

Taking the general antiderivative of αt we get,

α't=kt+v0, where v0 is the initial velocity.

As α't=vt,

vt=kt+v0,

We have v0=100

So, substituting t=0 in vt we get,

v0=k0+v0

v0=100

So, substitute value of v0 in v(t) we get,

vt=kt+100

When the car stops then the velocity will be vt=0 then t will be

0=kt+100

t=-100k

Now, taking the general antiderivative of vt

st=k

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