Question

A car moves along a straight line, whose equation of motion is given by $s-12t+3t^2-2t^2-2t^3$ where $s$ is in metres and t in seconds. The velocity of the car at the start will be

• A. $7m{s}^{-1}$
• B. $9m{s}^{-1}$
• C. $12m{s}^{-1}$
• D. $16m{s}^{-1}$

Answer 1

The correct option is C $12m{s}^{-1}$

The displacement-time equation is given by

$s-12t+3t^2-2t^2-2t^3=0$

$s=12t-3t^2+2t^2+2t^3$

Velocity, $v=\frac{ds}{dt}$

$v=12-6t-4t+6t^2$

The velocity of the car at the start will be

$v{|}_{t=0sec}=12-6\left(0\right)-4\left(0\right)+6(0{)}^2$

$v{|}_{t=0sec}=12m/s$

The correct option is C.