The distance s in metres covered by a particle in t seconds is \(s = \frac{3}{2}t^{2} - 3t\). Find its acceleration.
Question 1 Report
The distance s in metres covered by a particle in t seconds is \(s = \frac{3}{2}t^{2} - 3t\). Find its acceleration.
Answer Details
To find the acceleration, we need to differentiate the distance formula with respect to time (t):
\begin{align*}
s &= \frac{3}{2}t^{2} - 3t \\
\frac{d}{dt}s &= \frac{d}{dt}\left(\frac{3}{2}t^{2}\right) - \frac{d}{dt}(3t) \\
\frac{d}{dt}s &= 3t - 3 \\
\end{align*}
Therefore, the acceleration is the second derivative of the distance formula with respect to time:
\begin{align*}
\frac{d^{2}}{dt^{2}}s &= \frac{d}{dt}(3t - 3) \\
\frac{d^{2}}{dt^{2}}s &= 3 \\
\end{align*}
Thus, the acceleration of the particle is a constant value of 3 \(ms^{-2}\). Therefore, the answer is \(3 ms^{-2}\).
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