An athlete runs along a circular track of circumference 400m with a uniform speed 15m/s. What is the change in velocity when he runs through a distance of (i) 100m and (ii) 200m?
Answers
Answer:
The diameter of the circular track is given as 200 m. That is, 2r=200 m.
From this radius is calculated as Radius, r = 100 m.
In 40 sec the athlete complete one round. So, in 2 mins and 20 secs, that is, 140 sec the athlete will complete = 140 / 40 = 3.5 (three and a half) rounds.
One round is considered as the circumference of the circular track.
The distance covered in 140 sec = 2πr×3.5=2×3.14×100×3.5=2200 m.
For each complete round the displacement is zero. Therefore for 3 complete rounds, the displacement will be zero.
At the end of his motion, the athlete will be in the diametrically opposite position. That is, displacement = diameter = 200 m.
Hence, the distance covered is 2200 m and the displacement is 200 m.
Explanation:
Circumference of the track = 2*pi*r
= 2 * 3.14 * 100 m (as diameter is 200 m)
= 628 m
As the athlete covers one round in 40s, the speed of athlete,
S = Circumference/40s
Or, S = 628 m / 40 s
Or, S = 15.7 m/s ………. (1)
The distance covered by the athlete at the end of 2 min 20s (140 sec)
= 15.7 * 140 m
= 2198 m
So the distance covered = 2198 m
Now, 2198 m = 3* 628 + 0.5*628.
It means, the athlete has completed 3.5 rounds of the circular track at the end of 30 sec.
So, he/she is diametrically opposite of the starting point, at the end of 140 sec.
As, the displacement is the shortest distance between two points, in this case, it is 200 m (diameter).
So, Distance = 2198 m
Displacement - 200 m