Question

In a straight line motion, the distance travelled is proportional to the square root of the time taken. The acceleration of the particle is proportional to

• A. $\sqrt{v}$
• B. $v^2$
• C. $v^3$
• D. None of the above

Answer 1

Answer: (C)

$v^3$

$d\propto \sqrt{t}$

Then, velocity is $v=\frac{d\left(d\right)}{dt}\propto \frac{1}{2\sqrt{t}}$

Acceleration, $a=\frac{dv}{dt}\propto -\frac{1}{4(\sqrt{t}{)}^3}$

Hence, acceleration is proportional to $v^3$