# The integral ∫ 60 120 v ( t ) d t .

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 5, Problem 5RCC

(a)

To determine

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

Expert Solution

### Explanation of Solution

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:

60120v(t)dt (1)

Equation (1) represents the displacement of the particle from first to second minute duration.

Therefore, the displacement of the particle from first to second minute time duration is represented as 60120v(t)dt.

(b)

To determine

Expert Solution

### Explanation of Solution

Show the integral function as follows:

60120v(t)dt (2)

Equation (2) represents the total distance travelled by the particle from first to second minute duration.

The sum of the distance traveled by the particle in the straight line on time interval of t=60 to t=120seconds.

Therefore 60120|v(t)|dt represents the total distance of the particle moves from first to second minute along the straight line.

(c)

To determine

Expert Solution

### Explanation of Solution

The velocity is an integral of acceleration (a) over time (t).

Show the integral function as follows:

60120a(t)dt (3)

Equation (3) represents the velocity change of the particle from first to second minute duration.

Therefore 60120a(t)dt represents the rate of change in the velocity of particle on time interval of t=60 to t=120seconds.

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