JEE Main · PhysicsHard

$A particle starts from rest and moves with an acceleration a = k t, where k is a constant. What is the distance covered by the particle in time t ?$

Show correct answer & step-by-step solution

Correct answer: C — $\frac{k t ^{3}}{6}$

Solution

Integrating acceleration a = k t with respect to time gives velocity v = \int k t d t = \frac{k t ^{2}}{2} . Integrating velocity with respect to time gives displacement s = \int \frac{k t ^{2}}{2} d t = \frac{k t ^{3}}{6} .