Question

The first half of a certain path is covered with a velocity ‘v’ and the second half is covered with velocity ‘4v’. The average velocity of the journey is-

Answer 1

Average velocity of the journey is 1.6v m/s

Explanation :

Let the whole distance be s.

So, distance of 1st half = s/2

Distance of 2nd half = s/2

Velocity of 1st half = v

Velocity of 2nd half = 4v

We know, velocity = Displacement/Time

⇒ v = (s/2)/Time

⇒ Time × v = s/2

⇒ Time = (s/2)/v

⇒ Time 1 = s/2v ...(i)

Secondly, 4v = (s/2)/Time

⇒ Time × 4v = s/2

⇒ Time = (s/2)/4v

⇒ Time = s/8v ...(ii)

∴ Total time = (s/2v) + (s/8v)

= (4s + s)/8v

= 5s/8v

Now we know, av. velocity = Total displacement/Total time

⇒ Av. velocity = (s)/(5s/8v)

⇒ Av. velocity = s × (8v/5s)

⇒ Av. velocity = 8v/5

⇒ Av. velocity = 1.6v m/s

∴ Average velocity of whole journey = 1.6v m/s