Question

A displacement of a particle starting from rest t( t=0)is given by x=[6t2-t3) calculate the time at which the particle will attain 0 velocity again

Answer 1

x = 6t² - t³.....(1)

We know that,
dx/dt = v

From (1)-
d(6t² - t³)/dt = v
12t - 3t² = v........(2)
Now, the question says to find out a time when velocity (v) will again be 0.

So, put v = 0 in (2) equation.
12t - 3t² = 0
12t = 3t²
12 = 3t
t = 4sec.

Answer 2

Given,

x = 6t^2 - t^3.

velocity = dx/dt

dx/dt = 12t - 3t^2

so particle will attain velocity = 0

=) V = 12t - 3t^2

=) put V = 0

we get ,

=) 3t(4 - t) = 0

we get t = 0 and t = 4 sec

so at t = 0 particle starts and again attains zero velocity at t = 4 sec ..

____hope it will help u __________

◆ shreya ^_^