Question

A body travelling along a straight line traversed

one third of the total distance with a velocity of 4

m/s. The remaining part of the distance was

covered with a velocity 2 m/s for half the time and

with velocity of 6 m/s for the other half of the

time. The mean velocity averaged over the whole

time of motion is:

(a) 5 m/s (b) 4 m/s (c) 4.5 m/s (d) 3.5 m/s​

Answer 1

Answer:

Step-by-step explanation:

Let 'S' denote the total distance

Let time covered for first one third distance be t1

Then

according to given condition

         t1 = (S/3) / 4 = S / 12

Let t2 be time for next two journeys

     2S / 3 =2 t2 + 6 t2 = 8 t2

  ⇒       t2 = 2S / (12)

We know that

Average velocity = Total distance / Total time

                            =S / (t1 + 2 t2)

By putting

              t1 = S / 12

              t2 = 2 S / 12

we get    

Average velocity = S / { S / (12) + 2 S / (12)  }

                            = 4 m/s

Hence (B) is the correct answer