Question

The position of a particle is given by $S=f\left(t\right)=t^3-6t^2+9t$, $S$ is in meters, $t$ is in seconds, then the instantaneous velocity, when $t=2$ is ______

• A. $-2m/sec$
• B. $-1m/sec$
• C. $-3m/sec$
• D. $1m/sec$

Answer 1

The correct option is C $-3m/sec$

Instantaneous velocity is given by

$v=\frac{dS}{dt}=f^{\prime }\left(t\right)=3t^2-12t+9$

At $t=2s$

$f^{\prime }\left(2\right)=3(2{)}^2-12.2+9=12-24+9$

$⟹v=-3m/s$