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

Velocity is zero.

Step-by-step 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.(t^3)/(3)`

Put t = 0 we get:

`v=0\ m.s^(-1)`