Question

The motion of a particle along a straight line is described by the equation $x=6+27t-t^3$.
Find the time when $K.E$ of the particle is zero.

• A. $3s$
• B. $2s$
• C. $4s$
• D. $1s$

Answer 1

The correct option is A $3s$

The motion of the particle is given by $x=6+27t-t^3$
Its velocity, $v=27-3t^2$
Kinetic energy becomes zero when the velocity becomes zero.
$\therefore v=27-3t^2=0$
$t=+3,-3$
Time is always positive.
The $K.E$ of the particle becomes zero at $t=3s$