Question

A car moves with an average speed of a m/s during firsthalf of its journey and with bm/s during the remaining half. Calculate its average speed during the entire journey.

Answer 1

Answer:

4ab/(a+b)

Explanation:

Let the whole Distance be d m.

Then, For the first half Distance -

Distance = d/2 m

Speed = a m/s

So, Time = (d/2)/a

⇒ Time = d/(2a) seconds

For the second half Distance -

Distance = d/2 m

Speed = b m/s

So, Time = (d/2)/b

⇒ Time = d/(2b) seconds

Now, Average Speed = Total Distance/Total Time.

⇒ Avg. Speed = (d)/(d/2a + d/2b)

⇒ Avg. Speed = (d)/((xb + xa)/4ab)

⇒ Avg. Speed = [d/1]*[4ab/x(a +b)]

⇒ Avg. Speed = (4ab/a+b) m/s

Hence, the Average Speed during the entire journey is 4ab/(a+b) m/s.