Question

A travels some distance with a speed \[30\;{\rm{km/h}}\] and returns with the speed of \[45\;{\rm{km/h}}\]. Calculate the average speed of the train.

Answer 1

Hint: The above problem can be resolved by using the concepts and fundamentals related to the kinematics. In kinematics, the average speed is one of the most significant elements considered to solve the problems of average speed is to remember the formula. In the given problem, the two values of the velocity of the train are given, and the average of these two values will provide us with the required value of average speed.

Complete step by step answer:
Given:
The velocity of the train at travel is, \[{v_1} = 30\;{\rm{km/h}}\].
The velocity of the train on returning is, \[{v_2} = 45\;{\rm{km/h}}\].
Let us assume that the distance travelled by the train is l.
We know the formula for the time which is given by,
${t_1} = \dfrac{l}{{30}}$
We know the formula for the time which is given by,
${t_2} = \dfrac{l}{{45}}$
We know the expression for the average speed of train is,
\[{V_{av.}} = \dfrac{{2l}}{{{t_1} + {t_2}}}\]
Solve by substituting the value in the above expression as,
 \[\begin{array}{l}
{V_{av.}} = \dfrac{{2l}}{{\dfrac{l}{{30}} + \dfrac{l}{{45}}}}\\
{V_{av.}} = \dfrac{{2 \times 30\;{\rm{km/h}} \times 45\;{\rm{km/h}}}}{{30\;{\rm{km/h}} + 45\;{\rm{km/h}}}}\\
{V_{av.}} = 36\;{\rm{km/h}}
\end{array}\]
 Therefore, the average speed of the train is \[36\;{\rm{km/h}}\].

Note: To resolve the given problem, one must remember the concept of the average speed, along with the basic steps involved in the calculations. Moreover, let us take an example to understand the concept of the average speed. Consider a car travelling with some magnitude of velocity, and then it covers some other magnitude of velocity for another fraction of time and distances. Then to calculate the value of average speed, we need to sum up all the speeds and then take the average of the result.