If a particle moves in a straight line such that the distance travelled in time t is given by

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

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