Question

A car covers half of its total distance with speed v_1 and the rest half distance with speed v_2 . Its average speed during the complete journey is

Answer 1

Let, the total distance covered by the particle during the complete journey is 2x.

If The half distance (x) covered with the speed v1 in t1 time.

Using formula of speed, v1=x/t1

so, t1= x/v1

And another half distance (x), covered with speed v2 in time t2.

so, v2=x/t2

t2=x/v2

AVERAGE VELOCITY = Total distance /Total time

Total time= t1+t2 = x/v1 + x/v2

=(v2x+v1x)/v1v2

Total distance = x+x=2x

On putting the values of total distance and total time in the formula of average speed, we get

Average speed= 2x /(v2x+v1x / v1v2)

= 2v1v2 /(v1+v2)

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