Question:
If a particle moves in a straight line such that the distance travelled in time $t$ is given by $s=t^{3}-6 t^{2}+9 t+8$. Find the initial velocity of the particle.
Solution:
$s=t^{3}-6 t^{2}+9 t+8$
$\Rightarrow \frac{d s}{d t}=3 t^{2}-12 t+9$
Initial velocity $=$ Velocity at $t=0$
$\Rightarrow \frac{d s}{d t}=3(0)^{2}-12(0)+9$
$\Rightarrow \frac{d s}{d t}=9$ units/unit time