Question

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

Answer 1

Answer:

0 m/s

Explanation:

As per the provided information in the given question, we have :

• A body goes A to B with a velocity of 20m/s and comes back from B to A with a velocity of 30m/s.

We are asked to calculate the average velocity.

Average velocity is defined as total displacement divided by total time.

$\longmapsto \rm { Velocity_{(avg)} = \dfrac{Total \; displacement}{Total \; time} }$

So, in order to calculate average velocity, we need to find the total displacement and total time first.

Calculating total displacement :

Displacement is the shortest distance from initial position to the final position. When the body comes back to its initial position after covering certain distance then its displacement is 0.

⇒ Here, body's initial position is A and final position is B. And, it comes back again to A after covering certain distance m Therefore, total displacement is 0.

Calculating total time :

• In first case, velocity is 20 m/s.
• In second case, velocity is 30 m/s.

$\longrightarrow \sf { Velocity = \dfrac{Displacement}{Time} }$

$\longrightarrow \sf { Time = \dfrac{Displacement}{Velocity} }$

Let us assume the displacement made by body from A to B as 's'.

So, time taken to make the displacement form A to B :

$\longrightarrow \rm { t_1 = \dfrac{s}{20} \; s }$

And, time taken to make the displacement form B to A :

$\longrightarrow \rm { t_2 = \dfrac{s}{30} \; s}$

Now, the total time will be given by :

$\longmapsto \rm { Time_{(Total)} = t_1 + t_2 }$

$\longmapsto \rm { Time_{(Total)} =\Bigg ( \dfrac{s}{20} + \dfrac{s}{30}\Bigg )\; s}$

$\longmapsto \rm { Time_{(Total)} =\Bigg ( \dfrac{3s+2s}{60}\Bigg )\; s}$

$\longmapsto \rm { Time_{(Total)} =\Bigg ( \dfrac{5s}{60}\Bigg )\; s}$

$\longmapsto \bf { Time_{(Total)} = \dfrac{s}{12} \; s}$

∴ Total time taken in s/12 seconds.

$\rule{200}2$

Calculating average velocity :

$\longmapsto \rm { Velocity_{(avg)} = \Bigg ( 0 \div \dfrac{s}{12} \Bigg ) \; ms^{-1}}$

$\longmapsto \bf { Velocity_{(avg)} = 0 \; ms^{-1}}$

∴ Average velocity is 0 m/s.