# The velocity of the particle after t seconds . ### 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 3.4, Problem 69E
To determine

## To find: The velocity of the particle after t seconds.

Expert Solution

The velocity of the particle after t seconds is v(t)=2.5πcos(10πt) cm/s.

### Explanation of Solution

Given:

The equation of vibrating string is s(t)=10+14sin(10πt), where t is in seconds and s is in centimeters.

Recall:

If x(t) is a displacement of a particle and the time t is in seconds, then the velocity of the particle is v(t)=dxdt.

Calculation:

Obtain the velocity of the particle after t seconds.

v(t)=ddt(s(t))=ddt(10+14sin(10πt))=0+14cos(10πt)10π=5π2cos(10πt)

Therefore, the velocity of the particle after t seconds is v(t)=2.5πcos(10πt) cm/s.

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