A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is $x(t)=9 \sin t$ , where t is in seconds and x in centimeters. Find the velocity at time t.
A) $v(t)=9 \cos t$
B) $v(t)=2 \cos 9 t$
C) $v(t)=\cos 9 t$
D) $v(t)=9 \sin 9 t$
E) $v(t)=\sin 9 t$

Question

A mass on a spring vibrates horizontally on a smooth level surface (see the figure). Its equation of motion is $x(t)=9 \sin t$ , where t is in seconds and x in centimeters. Find the velocity at time t. 
A) $v(t)=9 \cos t$ 
B) $v(t)=2 \cos 9 t$ 
C) $v(t)=\cos 9 t$ 
D) $v(t)=9 \sin 9 t$ 
E) $v(t)=\sin 9 t$

Quizplus · Accepted Answer

We know that velocity is the derivative of displacement with respect to time.
Thus, $$v(t)=x'(t)=\frac{d}{dt}(9 \sin t)=9 \cos t$$
Therefore, the correct choice is A.

A Mass on a Spring Vibrates Horizontally on a Smooth x(t)=9sin⁡tx(t)=9 \sin tx(t)=9sint

A Mass on a Spring Vibrates Horizontally on a Smooth $x(t)=9 \sin t$