Relativity Series-1: Relative Motion

Relativity Series-1 Relative Motion

Place yourself in a moving car, when you see the person next to you, he appears to be at rest, but for someone standing on the footpath the same person appears to be moving at certain speed. Do we say the person is at rest or say he is moving? The answer can be found in something called as ‘relative motion’. We mentioned about relative motion during our Physics tuition class of Kinematics but let’s discuss it in detail what relative motion is and the concept of reference point.

Let’s say a car is moving at a speed of 10 km/h. Does the car appear to move at the same speed for everyone on the planet? The answer is a big ‘no’. So, who can see the object moving at 10 km/h? The reference (let’s say you). Speed is defined with respect to a reference and with respect to the reference the car we were discussing about is moving at 10 km/h. It need not appear to move at 10km/h for everyone. But for someone (say Mr. A) chasing the car at a speed of 3 km/h the car appears to move at a speed of 7 km/h.

We know that speed can be defined as the amount of distance travelled by a moving object per unit time. So for you, standing by the road the car appears to move at 10 km/h, here you are the reference point. You note initial distance between you and the car as ‘x’ and if note the distance after one hour it will ‘10+x’. Since distance travelled by the car is (10+x)-(x)=10, the speed of the car is given by 10km/h. In the second case where Mr. A is chasing the car at 3 km/h, say the initial distance between Mr. A and you is ‘y’, and the distance between the car and you is ‘x’. Since Mr. A is chasing the car, at any point of time the distance between Mr. A and the car is ‘(the distance between you and the car)-(the distance between you and Mr. A)’ (assuming all three of you are on a straight line with the car in the upfront followed by Mr. A followed by you.).

Initially the distance between Mr. A and the car is ‘x-y’ km. Now, in a span of one hour Mr. A travels a distance of 3 km and is y+3 km away from you. The car travels a distance of 10 km in the same time and is x+10 km from you. Distance between Mr. A and the car after one hour, as per the rule stated above, is (x+10)-(y+3) i.e., (x-y)+7 km. Since the initial distance between them is x-y km and the final distance is (x-y)+7 km. So as per Mr. A the car has travelled (x-y)+7-(x-y) km i.e., 7 km in a span of one hour. The speed of the car is 7 km/h as per Mr. A.

If Mr. A were travelling at 10 km/h, the final distance between Mr. A and car would be x-y and since the initial distance is also x-y, the distance travelled by the car with respect to Mr. A would be zero and hence for Mr. A the car appears like it is at rest. In reality where Mr. A is an actual person chasing a car on a road (with trees, shops and houses on its sides), it would appear counter-intuitive for Mr. A to say that the car isn’t moving. But, imagine the same on a plain road surrounded by nothing; doesn’t it make sense?