Question

A train travels from one station to another at a speed of $40kmh{{r}^{-1}}$ and returns to the first station at the speed of $60kmh{{r}^{-1}}$. Calculate the average speed and average velocity of the particular train.

Answer 1

Hint: The average speed is defined as the distance which is a scalar quantity per time ratio. On the other hand average velocity is the rate at which the position varies. That means the displacement varies. Average velocity is a vector quantity. Whereas average speed is a scalar one.

Complete step-by-step answer:
First of all let us discuss the average speed. Average speed is determined by dividing the total distance that something has travelled by the total amount of time to travel that distance completely. Average speed is usually applicable for vehicles like cars, trains, and airplanes. It is sometimes calculated in miles per hour or kilometres per hour. Average speed is a scalar quantity.
It is given by the formula
If the distance travelled are same, then,
$\dfrac{2{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}}=s$
Where${{v}_{1}}$, ${{v}_{2}}$ the different speeds.
And if the time taken to travel is same, then,
$\dfrac{\left( {{v}_{1}}+{{v}_{2}} \right)}{2}=s$
Where${{v}_{1}}$, ${{v}_{2}}$ the different speeds.
Here the distance travelled is same, therefore the average speed can be calculated as,
$\dfrac{2{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}}=s$
Substituting the values in it,
$\begin{align}
  & \dfrac{2\times 60\times 40}{60+40}=s \\
 & s=48kmh{{r}^{-1}} \\
\end{align}$
The average velocity of an object is defined as the total displacement of a body divided by the total time taken to travel. It is the rate at which an object varies its position from one place to the other.
Therefore it can be written as
$v=\dfrac{d}{t}$$v=\dfrac{d}{t}=0kmh{{r}^{-1}}$
Here the train is coming back to its original position, so the net displacement is zero. Therefore the average velocity will be also zero.
$v=\dfrac{d}{t}=0kmh{{r}^{-1}}$

 

Therefore the average speed will be $s=48kmh{{r}^{-1}}$ and average velocity will be zero.

Note: When an object moves to any other position, its displacement is given as the second position minus the first position. It is found to be always positive and is equal to the absolute value, or magnitude, of the displacement. Negative displacement is also there in which it means distance in the negative direction.