Two friends, A and B

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

Two friends, A and B, start cycling from the same point along the same straight road at t=0t=0. Their distance–time data are recorded as follows: Friend A: (0 s,0 m)(0\,\text{s},0\,\text{m}), (4 s,16 m)(4\,\text{s},16\,\text{m}), (8 s,32 m)(8\,\text{s},32\,\text{m}). Friend B: (0 s,0 m)(0\,\text{s},0\,\text{m}), (4 s,20 m)(4\,\text{s},20\,\text{m}), (8 s,28 m)(8\,\text{s},28\,\text{m}). Between the recorded points each friend moves with uniform speed. Answer the following questions. (i) Determine the uniform speed of each friend in the first 8 s8\,\text{s}. (ii) Who is cycling faster during this period and by how much? (iii) If both maintain their respective speeds beyond 8 s8\,\text{s}, at what time after the start will they be at the same distance from the starting point? (iv) Calculate that common distance. (v) Sketch qualitative distance–time graphs for both friends on the same axes and label the meeting point M (no numerical scales required).

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