Question

Derive the formula for average speed
1) if total distance divided into 3 equal parts.
2) if total time divided into 3 equal parts

Answer 1

Explanation:

The speed of an object is found out by dividing the distance that the object covers by the time in which the object takes to cover this distance. If ‘D’ is the distance traveled in some time ‘T’ then the speed of the object for this journey or ‘s’ is equal to s = D/T.

Average Speed

This is the simplest case. But what if there is an object that covers part of its journey with one speed and the other part with another speed? Let us say a train goes from station A to B in 2 minutes and from B to C in 3 minutes. If the distance between any two stations is 6km, what is the speed of the train?

Answer: Here you can’t use the formula directly because as you may have observed the train has a different speed from A to B than from B to C. In this case when a body has different speed during different parts of the journey, we define the average speed as:

Average Speed = (Total distance covered throughout the journey)/(Total time taken for the journey)

Let the body cover a distance ‘a’ in time t1, then a distance b in time t2, c in time t3 and so on, then the average speed of the body is found out by the following ratio:

Average speed = (a + b + c + …)/ (t1 + t2 + t3 + …). Let us see some examples now.