Q: A particle performs SHM with a period T and amplitude a. The mean velocity of the particle over the time interval during which it travels a distance a/2 from the extreme position is
(a) a/T
(b) 2a/T
(c) 3a/T
(d) a/2T
Ans: (c)
Sol: $\large y = a cos\omega t $
$\large a/2 = a cos\omega t $
$\large 1/2 = cos\omega t $
$\large cos\pi/3 = cos\omega t $
$\large t = \frac{\pi}{3\omega} = \frac{T}{6}$
Mean velocity $\large v_m = \frac{a/2}{T/6} = \frac{3a}{T}$