# The time duration for the particle to reach the velocity of 5 m / s . ### 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 3.8, Problem 7E

(a)

To determine

## To find: The time duration for the particle to reach the velocity of 5 m/s .

Expert Solution

The time duration for the particle to reach the velocity of 5m/s is 4s .

### Explanation of Solution

Given information:

The position function of a particle is given by,

s=t34.5t27t

The time duration for the particle to reach the velocity of 5m/s is calculated as,

s=t34.5t27tdsdt=3t29t75=3t29t7t23t4=0

Simplify further,

t=4s

Therefore, the time duration for the particle to reach the velocity of 5m/s is 4s .

(b)

To determine

### To find: The time duration for the particle to reach the acceleration zero.

Expert Solution

The time duration for the particle to reach the acceleration zero is 1.5s .

### Explanation of Solution

Given information:

The position function of a particle is given by,

s=t34.5t27t

The time duration for the particle to reach the acceleration zero is calculated as,

s=t34.5t27tdsdt=3t29t7d2sdt2=6t96t9=0

Simplify further,

t=1.5s

The significance at this value of t is that the velocity is at the minimum value.

Therefore, the time duration for the particle to reach the acceleration zero is 1.5s .

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