First slide

Average Velocity

Question

A car covers the first half of the distance between the two places at $40 {kmh}^{- 1}$ . and another half at $60 {kmh}^{- 1}$ . The average speed of the car is

Moderate

A

$40 {kmh}^{- 1}$
B

$48 {kmh}^{- 1}$
C

$50 {kmh}^{- 1}$
D

$60 {kmh}^{- 1}$

Solution

As from the question,
Average speed of the car, v_av
$= \frac{Total distance travelled by the body (d)}{Total time taken (t_{1} + t_{2})}$ …(i)
So, now time taken in 1st half of the distance,
   $t_{1} = Time = \frac{Distance}{Velocity} = \frac{d}{2 \times 40}$
$\Rightarrow$    $t_{1} = \frac{d}{80}$ $(∵ Distance = \frac{d}{2}, velocity = 40 {kmh}^{- 1})$
Time taken for 2nd half, $t_{2} = \frac{d}{2 \times Velocity}$
So,    $t_{2} = \frac{d}{2 \times 60} = \frac{d}{120}$
$(∵ distance = \frac{d}{2}, velocity = 60 {kmh}^{- 1})$
Now, average velocity, $v_{av} = \frac{d}{\frac{d}{80} + \frac{d}{120}}$ [From Eq. (i})
   $= \frac{d \times 80 \times 120}{200 d} = 48 {kmh}^{- 1}$

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