   Chapter 5.4, Problem 60E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
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) = t2 − 2t − 3, 2 ≤ t ≤ 4

(a)

To determine

To find:

The displacement of the particle.

Explanation

Given information:

The velocity function for a particle moving along a line is v(t)=t22t3.

The time interval is 2t4. Hence, the region lies between t1=2 and t2=4.

Calculation:

Find the displacement of the particle using the relation:

Displacement=t1t2v(t)dt (1)

Here, the velocity function is v(t).

Substitute (t22t3) for v(t), 2 for t1, and 4 for t2 in Equation (1).

Displacement=24(t22t3)dt (2)

Integrate Equation (2) and apply the upper and lower limits

(b)

To determine

To find:

The distance traveled by the particle during the time interval 2t4.

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