2026-09-10T00:15:11.984365 image/svg+xml Matplotlib v3.10.9, https://matplotlib.org/ © EAGLE BEACON GLOBAL Work out the values of \(t\) at which a particle ...
Question 1 Report
Work out the values of \(t\) at which a particle is at rest. The diagram shows \(s\) plotted against \(t\).
The particle moves along a straight line, and its displacement from a fixed point after \(t\) seconds is \(s = t^{3} - 6t^{2} + 9t\) metres.
Answer Details
A particle is at rest when its velocity is zero. Velocity is the rate of change of displacement:
\[v=\frac{ds}{dt}=3t^2-12t+9\] [M1][A1]
Set \(v=0\) and factorise:
\[3t^2-12t+9=0\]
\[3(t-1)(t-3)=0\] [M1]
Therefore:
\[t=1\text{ s}\quad\text{or}\quad t=3\text{ s}\] [A1]
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