Question

The motion of a particle along a straight line is described by the function $x=(2t-3{)}^2$ where $x$ is in meters and $t$ is in seconds. Find the velocity of the particle at the origin.

• A. $0\text{m/s}$
• B. $1\text{m/s}$
• C. $2\text{m/s}$
• D. $3\text{m/s}$

Answer 1

The correct option is A $0\text{m/s}$

Position of the particle is given by
$x=(2t-3{)}^2$
Time at which the particle is at origin will be given by
$0=(2t-3{)}^2$
$⟹t=\frac{3}{2}$
Velocity of the particle at any instant will be
$v=\frac{dx}{dt}=2(2t-3)\times 2=4(2t-3)$
At $t=\frac{3}{2}$ i.e. when the particle is at origin, $v=0$