Question

The velocity of a particle moving in a straight line varies with time in such a manner that `v` versus `t` graph is represented by one-half of an ellipse. The maximum velocity is `v_m` and the total time of motion is `t_0`
(i) average velocity of the particle is `(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 (ii) and (ii) are correct
D. both (i) and (ii) are wrong

Answer 1

Correct Answer - C
The displacement of the particle is determined by the area bounded by the curve, This area is : `s = (1)/(2) pi v_m (t_0)/(2)`
The average velocity is : `ltvgt = (s)/(t_0) = (pi)/(4) v_m`.
Such motion cannot be realized in practical terms since at the initial and final moments, the acceleration (which is slope of `v-t` graph) is infinitely large. Hence. both (i) and (ii) are correct, i.e., answer is ( c).