Question

A train takes 2 hours to reach station B from station A, and then 3 hours to return from station B to station A. The distance between the two stations is $200\text{ }km$. Find : (i) the average speed, (ii) the average velocity.

Answer 1

Hint: To calculate the average speed, calculate ratio of total distance travelled by the train and total time taken by train to complete the journey. For average velocity calculation, find the net displacement and divide by time taken.

Complete step-by-step answer:
Average speed of an object is given by total distance travelled by it in unit time. Mathematically, we can write this as
${{v}_{avg}}=\dfrac{d}{t}$
Where
${{v}_{avg}}=$ The average speed of the body
$d=$ Total distance travelled by the body
$t=$ Time taken
In this question, train travels first from A to B and then travels back from B to A. Therefore total distance travelled by the train is $d=200+200=400km$ and the total time it takes in the journey is $t=2+3\text{ hours}=5\text{ hours}$.

Thus the average speed of the train during the journey is
$\begin{align}
  & {{v}_{avg}}=\dfrac{400}{5}km\text{ }{{\text{h}}^{-1}} \\
 & \text{ = 80 km }{{\text{h}}^{-1}} \\
\end{align}$
Average velocity of the object is the net displacement of the object per unit time. As the train travels from A to B and then back to the same point/station. The net displacement of the train is zero. Therefore the average velocity of the train is also zero.

Additional Information:
Displacement is defined as the minimum distance between the final and initial positions of the object. Displacement is a vector quantity. Therefore velocity is also a vector.

Note: Sometimes students get confused and calculate average velocity as mean of the velocities in different time periods which is wrong. So try to avoid this mistake.
Velocity of an object is denoted by $\vec{v}\text{ or }\mathbf{v}$(bold-faced).