Question

the displacement of a particle starting from rest ( t=0) is given by x= 3tsquare - t cube calculate the time at which acceleration of the particle become zero​

Answer 1

Answer:

At t = 1 sec, the acceleration of the particle become zero

Explanation:

Given :

The displacement of a particle starting from rest (t = 0) is given by x = 3t² - t³

To find :

the time at which acceleration of the particle become zero​

Solution :

we get acceleration by differentiating velocity and the velocity by differentiating displacement.

Differentiating displacement,

v = dx/dt

 $\sf v=\dfrac{d}{dt} (3t^2-t^3) \\\\ \sf v=6t-3t^2$

Differentiating velocity,

a = dv/dt

$\sf a=\dfrac{d}{dt}(6t-3t^2) \\\\ \sf a=6-6t$

Now, we have to find the time at which acceleration of the particle becomes zero.

Put a = 0,

0 = 6 - 6t

6t = 6

 t = 6/6

 t = 1 sec

Therefore, at t = 1 the acceleration of the particle becomes zero