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

Question id: 573. This question is similar to one that appeared on an IB AA Standard paper in 2021. The use of a calculator is not allowed.

A particle travels in a straight line such that its displacement, \(s\) metres, from a fixed point, \(A\), after \(t\) seconds is given by \(s(t) = t^2 - 5t \), for \( 0 \le t \le 10\), as shown in the following sketch.

The particle starts at \(A\) and passes through \(A\) again when \(t = q\).

(a) Find the value of \(q\).

The particle changes direction when \(t = r\).

(b) Find the value of \(r\).

(c) Find the displacement of the particle from \(A\) when \(t = r\).

(d) Find distance of the particle from \(A\) when \(t=10\).

(e) Find the total distance travelled by the particle in ten seconds.

A second particle travels along the same straight line such that its velocity is given by \(v(t)=12 - 3t\) for \(t \ge 0\).

When \(t = p\), the distance travelled by this second particle is one metre less than the total distance travelled by the first particle in ten seconds.

(f) Find the value of \(p\)

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