Standard +0.3 This is a straightforward variable acceleration question requiring standard techniques: (a) solving a quadratic equation when v=0, and (b) finding when velocity is decreasing (v'<0), then integrating |v| over that interval. The quadratic factorizes nicely and the integration is routine, making this slightly easier than average for A-level.
A particle \(P\) moves along the \(x\)-axis so that its velocity \(v \mathrm {~ms} ^ { - 1 }\) at time \(t\) seconds \(( t \geqslant 0 )\) is given by
$$v = 3 t ^ { 2 } - 24 t + 36$$
a) Find the values of \(t\) when \(P\) is instantaneously at rest.
b) Calculate the total distance travelled by the particle \(P\) whilst its velocity is decreasing.
A particle $P$ moves along the $x$-axis so that its velocity $v \mathrm {~ms} ^ { - 1 }$ at time $t$ seconds $( t \geqslant 0 )$ is given by
$$v = 3 t ^ { 2 } - 24 t + 36$$
a) Find the values of $t$ when $P$ is instantaneously at rest.\\
b) Calculate the total distance travelled by the particle $P$ whilst its velocity is decreasing.
\hfill \mbox{\textit{WJEC Unit 2 2022 Q11}}