Acceleration is the rate of change of velocity with respect to time. In order to find the time at which the acceleration is zero, we need to find the time at which the rate of change of velocity is zero.

To find the acceleration, we need to differentiate the velocity function with respect to time.

Given: v = 2t^2 * e^-t

Differentiating v with respect to t gives:
a = d/dt (2t^2 * e^-t)
= 2 * d/dt (t^2) * e^-t + 2t^2 * d/dt (e^-t)
= 2 * 2t * e^-t + 2t^2 * (-e^-t)
= 4te^-t - 2t^2 * e^-t
= 2t * (2e^-t - t * e^-t)

Now, we need to find the value of t for which a = 0.

Setting a = 0, we have:
2t * (2e^-t - t * e^-t) = 0

This equation will be true if either 2t = 0 or (2e^-t - t * e^-t) = 0.

(1) When 2t = 0, we get t = 0.

(2) Now, let's solve the second equation:
2e^-t - t * e^-t = 0
e^-t(2 - t) = 0

This equation will be true if either e^-t = 0 or (2 - t) = 0.

e^-t = 0 does not have a real solution.

(2 - t) = 0 gives t = 2.

Therefore, the acceleration of the body is zero at t = 0 and t = 2.

------------------
- Acceleration is zero when the rate of change of velocity is zero.
- To find the time at which acceleration is zero, we differentiate the velocity function with respect to time.
- We find that the acceleration is given by a = 2t * (2e^-t - t * e^-t).
- Setting a = 0, we get 2t * (2e^-t - t * e^-t) = 0.
- This equation is satisfied when either 2t = 0 or (2e^-t - t * e^-t) = 0.
- The first equation gives t = 0.
- The second equation gives t = 2.
- Therefore, the acceleration of the body is zero at t = 0 and t = 2.