   Chapter 4.4, Problem 55E

Chapter
Section
Textbook Problem

# The velocity function (in meters per second) is given for a particle moving along a line. Find (a) the displacement and (b) the distance traveled by the particle during the given time interval. v ( t ) = 3 t − 5 ,    0 ≤ t ≤ 3

To determine

a)

To find:

The displacement.

Explanation

1) Concept:

vt=s't ;vt& st are the velocity and the displacement function of the particle respectively.

2) Given:

vt=3t-5, 0t3

3) Calculation:

The velocity of the particle moving along a line,

vt=3t-5, 0t3

To find the displacement of particle st, use vt=s't, i.e.,

vt=s't=3t-5, 0t3

So by using the Net change theorem s(x)-s(0)=0xs'(t)dt=0x(3

To determine

b)

To find:

The distance traveled by the particle during the given time interval.

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