Q. The acceleration of a particle increases linearly with time $t$ as 6$t$. If the initial velocity of the particle is zero and the particle starts from the origin, then the distance travelled by the particle in time $t$ will be
A) $t$
B) $t^{2}$
C) $t^{3}$
D) $t^{4}$
Explanation
(c) $\frac{dv}{dt} = 6t$ or $dv = 6t,mv = \frac{6t^{2}}{2} = 3t^{2}$,
$dx = 3t^{2}dt\ \Rightarrow \ x = 3\frac{t^{3}}{2} = t^{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.