Given the acceleration, a = d^2 s/d^ 2 = -4sin 2t, initial velocity v (0) = 2, and the initial position of the body as s (0) = -3. Find the body's position at time t.

Vivekanand Vellanki (last edited 2 years ago) (Expert, Founder @Qalaxia)

The approach to solve such questions is as follows.

You are given acceleration as a function of time. Integrating that function with respect to time gives Velocity as a function of time.

Integrating the velocity function with respect to time gives displacement as a function of time. This should help you find displacement given time.

v(0) and s(0) are given making it easy to find the constants in the integral.

Is this what you did?

It would be interesting to think about the kind of force that imparts this kind of acceleration.