Question

The displacement of a particle on a vibrating string is given by the equation s(t) = 2 + 1 5 sin(2πt) where s is measured in centimeters and t in seconds. Find the velocity of the particle after t seconds. v(t) = cm/s

Answer 1

Answer:

$v(t)= 30\pi cos(2\pi t)$

Step-by-step explanation:

The velocity of the particle is equal to the derivative of the displacement, so:

$v(t)=s'(t)$

Now, the derivative of s(t) is equal to:

$s'(t)=(2+15sin(2\pi t)'=0 + (15cos(2\pi t)*2\pi)=30\pi cos(2\pi t)$

Because we use the following properties:

If $f(t) = g(t) + h(t)$, then $f'(t) = g'(t) + h'(t)$

If $f(t) = a$, where a is a constant $f'(t) = 0$

If $f(t) = sin(t)$, then $f'(t) = cos(t)$

If $f(t) = sin(g(t))$, then $f'(t) = cos(g(t))*g'(t)$

Where f(t), g(t) and h(t) are functions of t.

So, the velocity of the particle after t seconds $v(t)$ is equal to:

$v(t)= 30\pi cos(2\pi t)$