Question

The distance between the two stations is $200km$. A train takes $2hours$ to cover the distance. Calculate the speed of the train.

Answer 1

Hint: In the question the information is given about the distance traveled by train between two stations and the time taken to cover the distance. We have been asked to calculate the speed of the train. We know, sped or velocity of an object is given by the ratio of the total distance to the time taken. So, we convert the values in the SI system of units and perform the calculation to get the speed.

Formula used: $v = \dfrac{d}{t}$
where $v$ is the velocity or speed, $d$ is the distance or displacement and $t$ is the time taken to cover the distance.

Complete step by step answer:
From the given question we have information about the distance traveled by train and the time taken by it to travel the distance. It is given that,
Total distance travelled $d = 200km$
Time taken to travel the distance $t = 2hrs$
We know, the velocity or speed is defined as the ratio of the total distance to that of the time taken to cover the total distance. So, we can calculate the speed of the train as:
$v = \dfrac{d}{t}$
We will calculate the speed in both the units of $kmh{r^{ - 1}}$and $m{s^{ - 1}}$.
In terms of $kmh{r^{ - 1}}$:
$ \Rightarrow v = \dfrac{{200}}{2}kmh{r^{ - 1}} = 100kmh{r^{ - 1}}$
In terms of $m{s^{ - 1}}$:
$d = 200km = 200 \times 1000m = 200000m$
$t = 2hrs = 2 \times 3600s = 7200s$
$\Rightarrow v = \dfrac{{200000}}{{7200}}m{s^{ - 1}} = 27.778m{s^{ - 1}}$
Thus, the speed of a train covering a distance of $200km$in $2hours$is $100kmh{r^{ - 1}}$or $27.778m{s^{ - 1}}$.

Note: If in a given question it is not asked to express the result in any particular unit, then it is always feasible to calculate the result in terms of SI units. Also, it must be kept in mind that though speed and velocity represent the same thing but the basic difference between the two is speed is a scalar quantity, i.e., it has only magnitude whereas velocity is a vector quantity, i.e., it has both magnitude and direction.