Question

If a particle moves in a straight line such that the distance travelled in time t is given by s = t³ − 6t² + 9t + 8. Find the initial velocity of the particle.

Answer 1

$$\begin{gathered} s=t^3-6t^2+9t+8 \\ \Rightarrow \frac{ds}{dt}=3t^2-12t+9 \\ \text{Initial velocity=Velocity at}\mathit{\text{t}}\text{=0} \\ \Rightarrow \frac{ds}{dt}=3{\left(0\right)}^2-12\left(0\right)+9 \\ \Rightarrow \frac{ds}{dt}\text{=9 units/unit time} \end{gathered}$$