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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 ?
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Solution
\[s = t^3 - 6 t^2 + 9t + 8\]
\[ \Rightarrow \frac{ds}{dt} = 3 t^2 - 12t + 9\]
\[\text { Initial velocity=Velocity at t }=0\]
\[ \Rightarrow \frac{ds}{dt} = 3 \left( 0 \right)^2 - 12\left( 0 \right) + 9\]
\[ \Rightarrow \frac{ds}{dt}=9 \text { units/unit time }\]
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