The displacement of a particle at any instant is given by x = 8t2 - 3t

1.	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 form t = 0 to t = 3s. 'x' is measured in m.
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. (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.

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 form t = 0 to t = 3s. 'x' is measured in m.

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.

(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.