A car travels along a straight road according to the following schedule: • • (it…

MATHEMATICS · Multi-part · A Level · Mathematics · Kinematics · Kinematics

Problem

A car travels along a straight road according to the following schedule: • 0≤t<2 s:  x=3t  m0\le t<2\,\text{s}:\;x=3t\;\text{m} • 2≤t<6 s:  x=6  m2\le t<6\,\text{s}:\;x=6\;\text{m} (it halts) • 6≤t≤10 s:  x=6−1.5(t−6)  m6\le t\le10\,\text{s}:\;x=6-1.5(t-6)\;\text{m}. (i) Plot a detailed position–time graph for 00–10 s10\,\text{s} on squared paper, choosing a convenient scale. (ii) Using only the coordinates of the endpoints of each time interval, calculate the average velocity in (a) 00–2 s2\,\text{s}, (b) 22–6 s6\,\text{s}, (c) 66–10 s10\,\text{s}. (iii) Find the average velocity for the whole motion from t=0t=0 to t=10 st=10\,\text{s} and interpret its sign. (iv) Which interval shows the greatest magnitude of average velocity? Give a reason based on your calculations and the graph.

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