Q: A particle performs SHM along a straight line with the period T and amplitude A. The mean velocity of the particle averaged over the time interval during which it travels a distance A/2 starting from the left extreme position is

(a) A/2T

(b) A/T

(c) 2A/T

(d) 3A/T

Ans: (d)

Sol:

$ \displaystyle x = Acos\omega t $

$\displaystyle A/2 = Acos\omega t $

$ \displaystyle \pi/3 = \omega t \, , t = \pi/3\omega$

$\displaystyle t = T/6 $

Mean velocity is

$\displaystyle v_m = \frac{A/2}{T/6} = 3A/T $