A spring-mounted slider moves horizontally. The displacement expression of the slider is

     s = 20 sin5t.

What is the slider's velocity and acceleration 2 seconds after it starts to move?

Let the velocity and acceleration of the slider be v and a, respectively. Let the time be t.

Since the first order derivative of the displacement with respect to time is velocity.

     v = ds/dt

Let θ = 5t, apply chain rule to calculate the velocity.

When time t = 2 sec,

     v = 100 cos5t = 100 cos10 cm/sec

As the second order derivative of the displacement with respect to time is acceleration.

Let θ = 5t, apply Chain Rule to calculate the acceleration.

When time t = 2 sec,

     s = -500 sin5t = -500 sin10 cm/sec²