A train takes 2 h to reach station B from station A, and then 3 h to return from station B to station A. The distance between the two stations is 200 km.

Find —

(i) The average speed

(ii) The average velocity of the train

Given,

Distance travelled S₁ = 200 km

time t₁ = 2 h

Distance travelled S₂ = 200 km

time t₂ = 3 h

(i) As we know,

$\text{Average speed} = \dfrac{\text{total distance}}{\text{total time taken}} \\[0.5em]$

Total distance travelled S = S₁ + S₂
= 200 km + 200 km
= 400 km

Total time taken t = t₁ + t₂
= 2 h + 3 h
= 5 h

Substituting the values of total distance travelled and total time taken in the formula of Average Speed above, we get,

$\text{Average speed} = \dfrac{400 \text { km}}{5 \text { h}} \\[0.5em] \Rightarrow \text{Average speed} = 80 \text { kmh} ^{-1} \\[0.5em]$

Hence, Average speed of the car = 80 km h^-1

(ii) Displacement = 0 (since final position is same as initial position)

Hence, Average velocity = 0 ( as displacement = 0)