Question

The displacement of a particle at any instant is given by x=8t²- 3t³. Calculate the average velocity in the interval from t =0 to t=2s and in

the time interval from t=0 to t=3s .​

Answer 1

Answer:

Here, x = 8t2 - 3t3 (i) when t = 0, x = 0 when t = 2s, x =8(2)2 - 3(2)3 = 32 - 24 = 8 m. Displacement in time interval (2 -0 = 2s) = 8m - 0 = 8 m. Average velocity = Displacement /Time interval = 8m/2s = 4 ms-1.

Answer 2

Here, x = 8t2 - 3t3 (i) when t = 0, x = 0 when t = 2s, x =8(2)2 - 3(2)3 = 32 - 24 = 8 m. Displacement in time interval (2 -0 = 2s) = 8m - 0 = 8 m. Average velocity = Displacement /Time interval = 8m/2s = 4 ms-1. (ii) When, t = 0, x = 0 when t = 3s, x = 8(3)2 -3(3)3 = 72 - 81 = -9m Net displacement = -9 - 0 = -9 m Time interval = 3 - 0 = 3s. Average velocity = -9m/3s = -3ms-1.