Question

The velocity of an object with a mass of `3 kg` is given by `v(t)= sin 2 t + cos 4 t`. What is the impulse applied to the object at `t= pi /4`?

Answer 1

There is no impulse at that time.

Explanation:

The acceleration, `a(t)`, is the first derivative of `v(t)`.

`a(t) = (dv(t))/dt = 2cos2t -4sin4t`

Evaluating that at time `t = pi/4`,

`a(pi/4) = 2cos(pi/2) - 4sinpi = 2*0 - 4*0 = 0`

Since the acceleration is zero, the force applied to this object is zero.

Now impulse. Impulse is `"force"*"time"`, where time is the length of time that the force was applied. The question does not refer to a time duration, just the moment when `t = pi/4`.

So "impulse" would not really apply to this situation even if the force had not calculated out to be zero.

I hope this helps,
Steve