Question

If velocity of a particle moving along a straight line changes with time as

V(m/s) = 4 sin (π/2)t, its average velocity over time interval t = 0 to t = 2(2n−1) sec, (n being any +ve integer) is,

• A. $\frac{8}{\pi(2n - 1)}$ m/s
• B. $\frac{4}{\pi(2n - 1)}$m/s
• C. Zero
• D. $\frac{16(2n - 1)}{\pi}$ m/s

Answer 1

Answer: (A)

$\frac{8}{\pi(2n - 1)}$ m/s

Answer 2

Displacement over the interval t = 0 to t = 2(2n − 1) seconds.

= $4\int_{0}^{2(2n - 1)}{\sin\left( \frac{\pi}{2}t \right)dt} = - \left( \frac{8}{\pi} \right)\left| \cos\left( \frac{\pi}{2}t \right) \right|_{0}^{2(2n - 1)}$

= $- \left( \frac{8}{\pi} \right)\left\lbrack \cos\pi(2n - 1) - \cos 0 \right\rbrack = \frac{16}{\pi}m$

⇒ average velocity = $\frac{16}{2(2n - 1)\pi}$ = $\frac{8}{(2n - 1)\pi}$m/s.,

Hence (1) is correct