A particle moves along a straight line such that its displacement at any time t is given by S=t3-6t2+3t+4. The velocity when the accelerations zero in m/s is:

Question

A particle moves along a straight line such that its displacement at any time t is given by S=t3-6t2+3t+4. The velocity when the accelerations zero in m/s is: (A) -9 (B) -12 (C) 42 (D) 3

Tardigrade Admin · Accepted Answer

Given s=t3-6t2+3t+4 (ds/dt)=3t2-12t+3 and (d2s/dt2)=6t-12 If acceleration is zero, 6t-12=0 or t=2 sec Hence, velocity at t = 2 sec v=(ds/dt)=3t2-12t+3 =12-24+3=- 9 m text/s

Q. A particle moves along a straight line such that its displacement at any time t is given by $S = t^{3} - 6 t^{2} + 3 t + 4.$ The velocity when the accelerations zero in m/s is:

-9

-12

42

3

Given $s = t^{3} - 6 t^{2} + 3 t + 4$ $\frac{d s}{d t} = 3 t^{2} - 12 t + 3$ and $\frac{d ^{2} s}{d t ^{2}} = 6 t - 12$ If acceleration is zero, $6 t - 12 = 0$ or $t = 2 sec$ Hence, velocity at t = 2 sec $v = \frac{d s}{d t} = 3 t^{2} - 12 t + 3$ $= 12 - 24 + 3 = - 9 m / s$

Q. A particle moves along a straight line such that its displacement at any time t is given by S=t3−6t2+3t+4. The velocity when the accelerations zero in m/s is:

-9

-12

42

3

Given s=t3−6t2+3t+4 dtds​=3t2−12t+3 and dt2d2s​=6t−12 If acceleration is zero, 6t−12=0 or t=2sec Hence, velocity at t = 2 sec v=dtds​=3t2−12t+3 =12−24+3=−9m/s

Q. A particle moves along a straight line such that its displacement at any time t is given by $S = t^{3} - 6 t^{2} + 3 t + 4.$ The velocity when the accelerations zero in m/s is:

Given $s = t^{3} - 6 t^{2} + 3 t + 4$ $\frac{d s}{d t} = 3 t^{2} - 12 t + 3$ and $\frac{d ^{2} s}{d t ^{2}} = 6 t - 12$ If acceleration is zero, $6 t - 12 = 0$ or $t = 2 sec$ Hence, velocity at t = 2 sec $v = \frac{d s}{d t} = 3 t^{2} - 12 t + 3$ $= 12 - 24 + 3 = - 9 m / s$