A particle moves along a straight line such that its displacement at any time t is given by s=t3-3t2+2m. The displacement when the acceleration becomes zero is:

Question

A particle moves along a straight line such that its displacement at any time t is given by s=t3-3t2+2m. The displacement when the acceleration becomes zero is: (A) zero (B) 2 m (C) 3 m (D) -2 m

Tardigrade Admin · Accepted Answer

Acceleration is equal to rate of change of velocity. Given,

s = t^{3} - 3 t^{2} + 2

Velocity

v = \frac{d s}{d t} = 3 t^{2} - 6 t

Acceleration

a = \frac{d ^{2} s}{d t ^{2}} = \frac{d v}{d t} = 6 t - 6

At

a = 0,

we have

6 t - 6 = 0

\Rightarrow t = 1 s

Hence,

s = (1)^{3} - 3 (1)^{2} + 2

= 1 - 3 + 2 = 0

Q. A particle moves along a straight line such that its displacement at any time t is given by s=t3−3t2+2m. The displacement when the acceleration becomes zero is:

zero

2 m

3 m

-2 m

Acceleration is equal to rate of change of velocity. Given, s=t3−3t2+2 Velocity v=dtds​=3t2−6t Acceleration a=dt2d2s​=dtdv​=6t−6 At a=0, we have 6t−6=0 ⇒t=1s Hence, s=(1)3−3(1)2+2 =1−3+2=0

Q. A particle moves along a straight line such that its displacement at any time t is given by $s = t^{3} - 3 t^{2} + 2 m .$ The displacement when the acceleration becomes zero is: