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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Suppose a particle moves back and forth along a straight line with velocity v(t), measured in feet per second, and acceleration a(t).

(a) What is the meaning of 60 120 v ( t ) d t ?

(b) What is the meaning of 60 120 | v ( t ) | d t ?

(c) What is the meaning of 60 120 a ( t ) d t ?

(a)

To determine

To define: The integral 60120v(t)dt.

Explanation

Given information:

The velocity of the particle over time is v(t). It is measured in feet per second.

The acceleration of the particle is a(t).

The particle is moves back and forth along the straight line.

The upper limit is 120 seconds (2 minute) and lower limit is 60 seconds (1 minute).

The displacement is an integral of velocity (v) over time (t).

Show the integral function as follows:

60<

(b)

To determine

To define: The integral 60120|v(t)|dt.

(c)

To determine

To define: The integral 60120a(t)dt.

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