Q. The equation of motion of a particle moving along a straight line is s=2$t^{3} - 9t^{2} + 12t,$ where the units of s and t are centimeter and second. The acceleration of the particle will be zero after
A) $\frac{3}{2}s$
B) $\frac{2}{3}s$
C) $\frac{1}{2}s$
D) 1s
Explanation
(a)
Given$\ s = 2t^{3} - 9t^{2} + 12t \Rightarrow \frac{ds}{dt} = 6t^{2} - 18t + 12\$
Again , $\frac{d^{2}s}{dt^{2}} = 12t - 18 = acceleration$
If acceleration becomes zero, then
$0 = 12t - 18 \Rightarrow t = \frac{3}{2}s$
Hence, acceleration will be zero after =$\frac{3}{2}s.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.