Question

An auto travels the first half time with a uniform speed '$a$' and the next half time with a uniform speed '$b$'. Find its average speed.

• A. $\frac{a+b}{2}$
• B. $2ab$
• C. $\frac{a-b}{2}$
• D. $ab$

Answer 1

The correct option is A $\frac{a+b}{2}$

Distance is given by the product of speed and time.

Let the total time of motion be $T$.
Distance moved in the first half time:
$d_1=aT/2$
Distance moved in the first half time:
$d_2=bT/2$
Total distance:
$d=aT/2+bT/2$
$d=\frac{T}{2}(a+b)$

By formula of average speed:
$v_{av}=\frac{d}{T}$
$v_{av}=\frac{\frac{T}{2}(a+b)}{T}$
$v_{av}=\frac{a+b}{2}$