Question

A body goes from C to D with a velocity of 20 m/ s and comes back from D to C with a velocity of 30 m/s . The average velocity of the body during the whole journey is.​

Answer 1

Answer:

$\boxed{Average \: speed = 24 \: m/s}$

Given:

Velocity of the body from C to D = 20 m/s

Velocity of the body from D to C = 30 m/s

To find:

Average velocity of the body

Step-by-step explanation:

Let distance between C to D be 'd'

So,

Total distance travelled by body = 2d

Let the time taken to travel from C to D be $t_{1}$

As, we know$speed = \frac{distance}{time}$

Therefore,

$\implies 20 = \frac{d}{t_{1}} \\ \\ \implies t_{1} = \frac{d}{20}$

Let the time taken to travel from D to C be $t_{2}$

Therefore,

$\implies 30 = \frac{d}{ t_{2}} \\ \\ \implies t_{2} = \frac{d}{30}$

Total time for covering 2d distance (t) = $t_{1} + t_{2}$

$Average \: speed = \frac{Total \: distance}{Total \: time} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{2d}{t} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{2d}{t_{1} + t_{2}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{2d}{ \frac{d}{20} + \frac{d}{30} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{2d}{ \frac{3d}{60} + \frac{2d}{60} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{2d}{ \frac{3d + 2d}{60} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{2d}{ \frac{5d}{60} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{2 \cancel{d} \times 60}{5 \cancel{d}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{2 \times 60}{5} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{120}{5} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 24 \: m/s$