Question

The displacement of a particle on a vibrating string is given by the equation s(t)=11+1/4sin(14PIt), where s is measured in centimeters and in seconds. Find the velocity of the particle after t seconds.

Answer 1

Find the first derivative of the given expression.

$s(t)=11+\frac{ 1 }{ 4}\sin(14{\pi}t) \\ \\s^{'}(t)=v(t)=\frac{ 7 }{ 2 }{\pi}\cos(14{\pi}t)$