Question

A car is moving in a circular path of radius 2m.

Calculate both the distance and the magnitude of displacement of the car after completing 1. One revolution

2. One half revolution

3. One fourth revolution.

What can you conclude about the relationship between the distance and displacement?

Answer 1

(1). When the car completes one revolution, the car would have completed a full circle then the distance would be the circumference of circle = 2×π×R = 2×3.14×2 = 12.56 m.

Also, the displacement is the shortest distance travelled between the initial and final point. Here initial and final points are the same. So Displacement = 0

(2). When the car would have completed a semi-circle then the distance would be the circumference of the semi-circle = πR = 3.14×2 = 6.28 m.

Also, the displacement is the shortest distance travelled between the inital and final point which is equal to the diameter of the circle = R +R = 2R = 2×2 = 4 m.
(3). Here the car would have completed a quarter circle.
Distance = πR/2 = 3.14×2/2 = 3.14 m.
Displacement = $\sqrt{(R^2+R^2)}=\sqrt{(2^2+2^2)}=\sqrt{8}=2.828m$.

Distance and displacement are used to indicate the length between two points. However, these two are not one and the same thing. While distance is the length of the actual path between two locations, displacement, on the other hand, is the length of the shortest path between two locations.