Question

Displacement of a particle starting from rest at t=0 is given by x=6t^2-t^3 calculate the time at which the particle will attain zero velocity again

Answer 1

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x = 6t²-t³

To find velocity at any instant, we will have to different displacement with respect to time.

$\frac{d}{dt} (6 {t}^{2} - {t}^{3} ) \\ = 2 \times 6t - 3 \times {t}^{2} \\ = 12t - 3 {t}^{2}$
So velocity at any instant is 12t-3t².

12t-3t² = 0
3t²-12t = 0
3t(t-4) = 0
3t = 0 or t-4 = 0

So the velocity will be 0 at t = 0 and t = 4

The velocity will be 0 after 4 seconds.

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Answer 2

displacement of particle is given by...

s=6t^2-t^3

differentiate wrt time..

ds/dt =12t-3t^2

v=12t-3t^2

velocity will be zero..

12t-3t^2=0

t(12-3t)=0

t=0 or 12-3t=0

t=0 or t=4