A particle moves along a straight line with equation of motion $s = t ^ { 3 } - t ^ { 2 }$ . Find the value of t at which the acceleration is equal to zero.
A) $- \frac { 2 } { 3 }$
B) $- \frac { 1 } { 3 }$
C) $\frac { 2 } { 3 }$
D) $\frac { 1 } { 3 }$
E) $- \frac { 1 } { 2 }$
F) $\frac { 1 } { 2 }$
G) $- \frac { 3 } { 2 }$
H)
$\frac { 3 } { 2 }$

Question

A particle moves along a straight line with equation of motion $s = t ^ { 3 } - t ^ { 2 }$ . Find the value of t at which the acceleration is equal to zero.
A) $- \frac { 2 } { 3 }$
B) $- \frac { 1 } { 3 }$
C) $\frac { 2 } { 3 }$
D) $\frac { 1 } { 3 }$ 
E) $- \frac { 1 } { 2 }$
F) $\frac { 1 } { 2 }$ 
G) $- \frac { 3 } { 2 }$ 
H)
$\frac { 3 } { 2 }$

Quizplus · Accepted Answer

The acceleration is the second derivative of the position function $s(t) = t^3 - t^2$. First, find the velocity $v(t) = 3t^2 - 2t$, then the acceleration $a(t) = 6t - 2$. Set $a(t) = 0$ to find $t = \frac{1}{3}$.

A Particle Moves Along a Straight Line with Equation of Motion