A particle $$\(P\)$$ moves in a straight line. The velocity $$\(v \mathrm{~m} \mathrm{~s}^{-1}\)$$ at time $$\(t \mathrm{~s}\)$$ is given by $$\[ \begin{array}{ll} v=2 t+1 & \text { for } 0 \leqslant t \leqslant 5, \\ v=36-t^{2} & \text { for } 5 \leqslant t \leqslant 7, \\ v=2 t-27 & \text { for } 7 \leqslant t \leqslant 13.5 . \end{array} \]$$ Find the total distance travelled by $$\(P\)$$ in the interval $$\(0 \leqslant t \leqslant 13.5\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s20_qp_42 Year：2020 Question No：6(c)
Answer:
$s=\int_{0}^{5}(2 t+1) \mathrm{d} t+\int_{5}^{6}\left(36-t^{2}\right) \mathrm{d} t+\left|\int_{6}^{7}\left(36-t^{2}\right) \mathrm{d} t+\int_{7}^{13.5}(2 t-27) \mathrm{d} t\right|$
$s=\int_{0}^{5}(2 t+1) \mathrm{d} t+\int_{5}^{6}\left(36-t^{2}\right) \mathrm{d} t+\left|\int_{6}^{7}\left(36-t^{2}\right) \mathrm{d} t+\int_{7}^{13.5}(2 t-27) \mathrm{d} t\right|$
$
s=\left[t^{2}+t\right]+\left[36 t-\frac{t^{3}}{3}\right]+t^{2}-27 t
$
All correct
$
s=84.25
$
$s=\int_{0}^{5}(2 t+1) \mathrm{d} t+\int_{5}^{6}\left(36-t^{2}\right) \mathrm{d} t+\left|\int_{6}^{7}\left(36-t^{2}\right) \mathrm{d} t+\int_{7}^{13.5}(2 t-27) \mathrm{d} t\right|$
$
s=\left[t^{2}+t\right]+\left[36 t-\frac{t^{3}}{3}\right]+t^{2}-27 t
$
All correct
$
s=84.25
$
Knowledge points:
4.2.3 use differentiation and integration with respect to time to solve simple problems concerning displacement, velocity and acceleration Calculus required is restricted to techniques from the content for Paper 1: Pure Mathematics 1.
Solution:
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