   Chapter 5.4, Problem 59E ### 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) = 3t − 5, 0 ≤ t ≤ 3

(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)=3t5.

The time interval is 0t3. So the region lies between t1=0 and t2=3.

Find the displacement of the particle using the relation:

Displacement=t1t2v(t)dt (1)

Here, the velocity function is v(t).

Substitute 3t5 for v(t), 0 for t1 and 3 for t2 in Equation (1).

Displacement=03(3t5)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 0t3.

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