Question

The velocity of a particle moving in a straight line varies with time in such a manner that $v$ versus $t$ graph is velocity is $v_{m}$ and the total time of motion is $t_{0}$

(i) Average velocity of the particle is $\frac{\pi}{4} v_{m}$
(ii) Such motion cannot be realized in practical terms

• A. Only (i) is correct
• B. Only (ii) is correct
• C. Both (i) and (ii) are correct
• D. Both (i) and (ii) are wrong

Answer 1

Answer: (C)

The displacement of the particle is determined by the area bounded by the curve. This area is
$s=\frac{\pi}{4} v_{m} t_{0}$
The average velocity is
$\langle v\rangle=\frac{s}{t_{0}}=\frac{\pi}{4} v_{m}$
Such motion cannot be relized in practical terms since at the initial and final moments, the acceleration (which is slope of $v$ -t graph) is infinitely large.