Standard +0.8 This question requires finding when velocity changes sign (factoring v(t) = (t-1)(t-4) to find zeros at t=1,4), then integrating |v| over separate intervals [1,4] and [4,5.5] where the particle changes direction. While the integration itself is routine, recognizing the need to split at direction changes and handle absolute values elevates this above a standard integration question.
3. A particle \(P\) moves along a straight line such that at time \(t\) seconds its velocity \(v \mathrm {~ms} ^ { - 1 }\) is given by:
$$v ( t ) = t ^ { 2 } - 5 t + 4$$
Find the distance travelled by the particle between \(t = 1\) and \(t = 5.5\). [0pt]
3. A particle $P$ moves along a straight line such that at time $t$ seconds its velocity $v \mathrm {~ms} ^ { - 1 }$ is given by:
$$v ( t ) = t ^ { 2 } - 5 t + 4$$
Find the distance travelled by the particle between $t = 1$ and $t = 5.5$.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM Mechanics 2021 Q3 [6]}}