Solveeit Logo
Login

Question

Question: The distance between the two stations is \(200km\). A train takes \(2hours\) to cover the distance. ...

The distance between the two stations is 200km200km. A train takes 2hours2hours to cover the distance. Calculate the speed of the train.

Explanation

Solution

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=dtv = \dfrac{d}{t}
where vv is the velocity or speed, dd is the distance or displacement and tt 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=200kmd = 200km
Time taken to travel the distance t=2hrst = 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=dtv = \dfrac{d}{t}
We will calculate the speed in both the units of kmhr−1kmh{r^{ - 1}}and ms−1m{s^{ - 1}}.
In terms of kmhr−1kmh{r^{ - 1}}:
⇒v=2002kmhr−1=100kmhr−1\Rightarrow v = \dfrac{{200}}{2}kmh{r^{ - 1}} = 100kmh{r^{ - 1}}
In terms of ms−1m{s^{ - 1}}:
d=200km=200×1000m=200000md = 200km = 200 \times 1000m = 200000m
t=2hrs=2×3600s=7200st = 2hrs = 2 \times 3600s = 7200s
⇒v=2000007200ms−1=27.778ms−1\Rightarrow v = \dfrac{{200000}}{{7200}}m{s^{ - 1}} = 27.778m{s^{ - 1}}
Thus, the speed of a train covering a distance of 200km200kmin 2hours2hoursis 100kmhr−1100kmh{r^{ - 1}}or 27.778ms−127.778m{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.