Question

an athlete completes one round of a circular track of radius R in 40 seconds. What will be the displacement at the end of 2 minutes , 20 seconds?

Answer 1

athlete angular speed = ω = 2 π / 40  = π / 20  sec^-1
the angular position Ф after 2 min 20 sec = π/20 * 140 = 7 π  This is equivalient to π.
So he/she is at the opposite end of the circular track from where he/she started.
Displacement = - 2 R = - diameter.    -ve.

Answer 2

Listen (i mean read)

2 minute 20 sec (in seconds)= 120 + 20 = 140 seconds 

Since the object (athelete) takes one round in 40 sec then 

By calculation and some common sense we could say that after 140 sec he would complete half round. which is equal to diameter.

Answer 3

speed = 2πr/40 m/s
let r = R
so distance covered in time 140 sec = 2πr/40 × 140
                                                     =  7πr m
so (6πr +πr) m
so displacement = 2R