Question

an athlete completes one round of a circular track of diameter 49 m in 20 seconds calculate the distance and displacement at the end of 30 seconds

Answer 1

Given, time = 2 min 20 secs = (2×60)+20=120+20=140 sec.Now, time taken to complete 1 round = 40 s, so total rounds completed in 140 s = 140/40 = 7/2 =3.5Now distance traveled in 1 round = 2ππr = 2×3.14×100 = 628 m .(since radius, r = diameter/2 =200/2 =100 and ππ=3.14 (approx.) ).Thus, total distance traveled in 2 min & 20 secs = 3.5 × 628 = 2198 m(2.2 km approximately).Now, for calculating displacement, consider this: After 3 complete rounds, the athlete returns to the point where he started, and then he completes the remaining 1/2 round, i.e. covers half of the circumference and thus reaches the diametrically opposite point (as shown in the figure);Now, the shortest distance between his initial and final position (i.e. the displacement) is the diameter = 200 m.Thus, the athlete's displacement is 200 m