Question

The acceleration of a particle is given by a = -kt^2, where a is in meters per second squared and the time t is in seconds. If the initial velocity of the particle at t=0 is__________.

Answer 1

Answer:

Velocity is zero.

Explanation:

Given:

• acceleration of particle, $a=-k.t^2\ m.s^{-2}$

• time of observation, $t=0\ s$

We know that acceleration is defined as the rate of change in velocity and hence we integrate the expression of acceleration.

Now the velocity can be given as:

$v=\int\limits {a} .\, dt=-k.\frac{t^3}{3}$

Put t = 0 we get:

$v=0\ m.s^{-1}$