#### To determine

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

#### Answer

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

#### Explanation

**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.