Damped oscillations — UPSC Physics Optional CSE 2020 Paper I

The equation for displacement (X) of a point on a damped oscillator is given by x = 5e^{-0.25t}\sin\left(\frac{\pi}{2}\right)t\ \text{metres}. Find the velocity of oscillating point at t = \frac{T}{4} and T, where T is the time period of the oscillator. What is the direction of velocity in each case?