## Exam-Style Question on Kinematics## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 598. This question is similar to one that appeared on an IB AA Standard paper in 2021. The use of a calculator is allowed.

A particle P moves along the x-axis. The velocity of P is \(v\)ms^{-l} at time \(t\) seconds,
where \(v(t) = 5 + 3t - 2t^2\) for \(0 \le t \le 3\). When \(t = 0\), P is at the origin O.

(a) Find the value of \(t\) when P reaches its maximum velocity.

(b) Find the distance of P from O at this time.

(c) Sketch a graph of \(v\) against \(t\), clearly showing any points of intersection with the axes.

(d) Find the total distance travelled by P.

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