A particle moves along a straight line with equation of motion $s = t ^ { 2 } - 3 t + 2$ . Find the value of t at which the particle reverses its direction.
A) $\frac { 1 } { 2 }$
B)0
C) $\frac { 3 } { 2 }$
D) $\frac { 2 } { 3 }$
E)1
F)2
G) $\frac { 3 } { 4 }$
H)
$\frac { 4 } { 3 }$

Question

A particle moves along a straight line with equation of motion $s = t ^ { 2 } - 3 t + 2$ . Find the value of t at which the particle reverses its direction.
A) $\frac { 1 } { 2 }$ 
B)0
C) $\frac { 3 } { 2 }$
D) $\frac { 2 } { 3 }$
E)1
F)2
G) $\frac { 3 } { 4 }$
H)
$\frac { 4 } { 3 }$

Quizplus · Accepted Answer

The direction of a particle reverses when its velocity changes sign, which occurs at the critical points of the velocity function. The velocity is the derivative of the position function $s(t) = t^2 - 3t + 2$, so $v(t) = \frac{ds}{dt} = 2t - 3$. Setting $v(t) = 0$ to find when the velocity is zero (and thus potentially changes direction), we get $2t - 3 = 0$, solving for $t$ gives $t = \frac{3}{2}$.

A Particle Moves Along a Straight Line with Equation of Motion