A walker moves along a straight north–south track in three stages

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

Problem

A walker moves along a straight north–south track in three stages. In stage 1 he walks a distance dd due north in time t1t_1. In stage 2 he walks the same distance dd due south in time t2t_2. In stage 3 he walks a distance d2\dfrac{d}{2} due north in time t3t_3. (a) Express the total distance travelled, the net displacement, and the total time of travel in symbolic form using d, t1, t2d,\,t_1,\,t_2 and t3t_3. (b) Using the results of part (a), obtain symbolic expressions for (i) the average speed and (ii) the average velocity of the walker for the complete motion. (c) If d=12 kmd = 12\,\text{km}, t1=30 mint_1 = 30\,\text{min}, t2=20 mint_2 = 20\,\text{min} and t3=10 mint_3 = 10\,\text{min}, calculate the numerical values of the average speed and the magnitude of the average velocity.

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