Question

A body covers half of its journey with speed
a m/s (variable) and the other half with b m/s (variable). Calculate the average speed of the object during the whole journey.

Answer 1

Dear Student

Let the distance be d,
For distance d/2;
Speed s₁=a m/s and
The time taken to cover this distance will be
$t_1=\frac{d/2}{s_1}=\frac{d}{2a}$
For the another half distance d/2;
Speed s₂= b m/s and
The time taken to cover this distance will be
$t_2=\frac{d/2}{s_2}=\frac{d}{2b}$
So the total distance = d/2+d/2 = d
The average Speed to travel the distance
d = $\frac{Totaldis\tan ce}{totaltime}=\frac{d}{{\displaystyle \frac{d}{2a}+\frac{d}{2b}}}=\frac{d}{{\displaystyle \frac{d\left(2b+2a\right)}{4ab}}}=\frac{2ab}{a+b}m/s$

Regards