A particle moves in a straight line through the point $$\(O\)$$. The displacement of the particle from $$\(O\)$$ at time $$\(t \mathrm{~s}\)$$ is $$\(s \mathrm{~m}\)$$, where $$\[ \begin{array}{ll} s=t^{2}-3 t+2 & \text { for } 0 \leqslant t \leqslant 6, \\ s=\frac{24}{t}-\frac{t^{2}}{4}+25 & \text { for } t \geqslant 6 . \end{array} \]$$ Find the total distance travelled by the particle in the first 10 seconds of its motion. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No:9709_m20_qp_42 Year:2020 Question No:7(c)
Answer:
At \(t=0, s=2\) or at \(t=6, s=20\)
At \(t=1.5, s=-0.25\)
At \(t=10, s=2.4\)
\([\) Total distance \(=2+0.25+0.25+20+(20-2.4)]\)
So total distance travelled \(=40.1 \mathrm{~m}\)
At \(t=1.5, s=-0.25\)
At \(t=10, s=2.4\)
\([\) Total distance \(=2+0.25+0.25+20+(20-2.4)]\)
So total distance travelled \(=40.1 \mathrm{~m}\)
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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