Question

A particle travels first half of the total time with speed v_1 and second half time with speed v_2. Find the average speed during the complete journey.

Answer 1

Answer:v1+v2/2 is the mean speed

Answer 2

Given:

A particle travels first half of the total time with speed v_1 and second half time with speed v_2.

To Find:

The average speed during the complete journey.

Solution:

Let total time taken be '2t' sec

Given, for first t sec , speed is V1 and for last t sec , speed is V2

Let

• distance covered , in first t sec = d1

• distance covered , in last t sec = d2
• Total distance = d1 + d2

We know

• Speed = distance/time
• Average speed = total distance/total time

Now,

• d1 = V1xt = V1t
• d2 = V2xt = V2t

Average Speed is given by,

• V = d1 + d2 / 2t = V1t + V2t / 2t = (V1 + V2)/2