Question

1. An athlete completes one round of a circular track of diameter
200 m in 40 s. What will be the distance covered and the
displacement at the end of 2 minutes 20 s?
2. Joseph jogs from one end A to the other end B of a straight
300 m road in 2 minutes 30 seconds and then turns around
and jogs 100 m back to point C in another 1 minute. What are
Joseph's average speeds and velocities in jogging (a) from A to
B and (b) from A to C?​

Answer 1

Answer:

1 .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.

2.From pont A to B

Distance covered=300m

Displacement=300m

Time taken=2 min 30 sec=(2×60)+30=150 sec

Average speed= Distance covered /Timetaken  = 300/150  =2 m/sec

Average velocity= Displacement/Timetaken  = 300/150  =2 m/sec

From point A to C

Distance covered=300+100=400m

Displacement=300−100=200m

Time taken=3 min 30 sec=(3×60)+30=210 sec

Average speed= Distance covered/Timetaken  = 210/400  =1.90 m/sec

Average velocity= Displacement/Timetaken  = 200/210

 =0.95 m/sec

Explanation: