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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

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 ) = t 2 2 t 3 ,    2 t 4

To determine

a)

To find:

The displacement.

Explanation

1) Concept:

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

2) Given:

vt=t2-2t-3,  2t4

3) Calculation:

The velocity of the particle moving along a line,

vt=t2-2t-3, 2t4 

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

 vt=s't=t2-2t-3, 2t4 

 st=03vtdt=03s'tdt

Substitute the value s't=t2-2t-3

To determine

b)

To find:

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

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