Question

If a point is moving in a line so that its velocity at time t is proportional to the square of the distance covered, then its acceleration at time t varies as

• A. cube of the distance
• B. the distance
• C. square of the distance
• D. none of these

Answer 1

The correct option is A cube of the distance

Velocity $v\propto s^2$
$v=k{s}^2$
$a=\frac{dv}{dt}=2ks\frac{ds}{dt}$
$\Rightarrow a=2ksv$
$\Rightarrow a=2k^2{s}^3$
Acceleration $a\propto s^3$