 # Exam-Style Question on Kinematics

## A mathematics exam-style question with a worked solution that can be revealed gradually

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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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