Question

A train travels with a speed of 60 km h-1 from station A to B and then comes back with speed 80 km h-1 from station B to station A. Find 1 - average speed and 2- the average velocity of train.

Answer 1

$\bf \underline{We \: have \: given \: that}$

• Spreed of train from A to B = 60km/h
• Speed of train from B to A = 80km/h

$\bf \underline{SOLUTION}$

Let the distance be x.

∴ (Distance between A to B) = (Distance between B to A) = x km.

We know that,

$\implies \small \boxed { \sf{time \: = \frac{distance}{speed} }}$

So,

Given Distance is x km and Speed is 60 and 80km/h.

➸ From A to B, Time = x/60 hrs

➸ From B to A, Time = x/80 hrs

➸ Total Time taken by train:

$\sf \dfrac{x}{80} + \dfrac{x}{60} = \dfrac{60x + 80x}{4800} = \bf{\dfrac{7x}{240} hrs}$

ㅤ

Q-1. Average speed of train?

$\sf\implies \small \boxed{ \sf{avg \: speed = \frac{total \: distance}{total \: time}} }$

$\sf \implies \: \dfrac{2x}{ \frac{7x}{240} }$

$\large \small \implies \boxed {\boxed {\bf \red {\dfrac{480}{7} \: or \: 68.5 km/hr }}}$

Q-2. Average Velocity of train?

Displacement is zero because train moves through same distance twice.

∴ Displacement = 0

$\large \small \implies \boxed {\boxed {\bf \red{Avg \: velocity = 0}}}$