   Chapter 3.9, Problem 60E

Chapter
Section
Textbook Problem

# Show that for motion in a straight line with constant acceleration a, initial velocity v 0 , and initial displacement s 0 , the displacement after time t is s = 1 2 a t 2 + v 0 t + s 0

To determine

To show:

The displacement after time is

s=12αt2+v0t+s0

Explanation

1) Concept:

i. 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.

ii.

at=ddxvt

iii.

vt=ddxst

2) Given:

Constant acceleration α, initial velocity v0, and initial displacement s0

3) Calculation:

Here, constant acceleration α, initial velocity v0, and initial displacement s0

The acceleration is constant for all t,

αt=a, where a  is a constant

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