Question

an athlete completes one round of a circular track of a diameter 200 m in 40 seconds what will be the distance covered and the displacement at the end of 2 minutes 20 seconds

Answer 1

Given, diameter, d of the circular track = 200 m.

Therefore, radius, r = 200 m/2 = 100 m

Time, t to complete one round = 40 s

Thus, in 2 minute 20 s = 2 × 60 + 20 = 140 s

Distance covered, s =?

Displacement =?

Circumference of the circular path is the distance covered by athletes to complete one round.

We know that, circumference of circle = 2πr2πr

∴ Circumference = 2xxpixx100\ m`

∴ Circumference = 200\ pi\ m`

Now, ∵ In 40 s athlete cover a distance of 200 π m200 π m

∴ In 1 s distance covered by the athlete =200 π m40 s=200 π m40 s

∴ In 140 s distance covered by the athlete =200 π m40 s×140 s=200 π m40 s×140 s

=200 m×140 s×2240 s×7=200 m×140 s×2240 s×7

=5 m×20×22=2200 m=5 m×20×22=2200 m

Now, number of rounds =Total distancecircumference=Total distancecircumference

=2200 m200 π=2200 m200 π

=2200 m200×22/7=2200 m200×22/7

=2200 m×7200×22=3.5=2200 m×7200×22=3.5 round

Thus, in given time of 2 minute 20 second, athlete will complete 3.5 rounds to the circular trak.

3.5 rounds means three rounds and half round. This means after the 3.5 rounds athlete will be just opposite to the starting point.

Just opposite to the starting point means, the displacement is equal to the diameter of circular path.

Thus, distance covered = 2200 meter and displacement = 200 m Answer

Answer 2

here, time = 2 minutes 20 seconds
= 2× 60sec + 20sec
= 140sec
now, in 40sec, the no. of round = 1
In 140sec, the no. of round= 1/40× 140= 3.5
diameter= 200m, so radius= 100
now,
distance covered in 1 round = circumference
= 2πr
=2× 22/7 × 3.5
= 2200m

calculation of displacement in 3.5 rounds :
the initial point is A and final point is B. therefore, displacement = AB
so, the displacement will be equal to diameter of the circular track which is 200m