Question

The displacement of a particle on a vibrating string is given by the equation s(t)=3+ \frac{1}{5} sin (3πt)
where s is measured in centimeters and t in seconds. Find the velocity (in cm/s) of the particle after t seconds.$\frac{1}{5}$

Answer 1

Answer:

  $v(t)=\dfrac{3\pi}{5}\cos{(3\pi t)}$

Step-by-step explanation:

The velocity is the derivative of position.

  $s(t)=3+ \dfrac{1}{5} \sin{(3\pi t)}\\\\v(t)=s'(t)=\dfrac{1}{5}(3\pi)\cos{(3\pi t)}\\\\\boxed{v(t)=\dfrac{3\pi}{5}\cos{(3\pi t)}}$