Question

A train running at the speed of $60km/hr$ crosses a pole in $9s$ . What is the length of the train?
A) $120metres$
B) $180metres$
C) $324metres$
D) $150metres$

Answer 1

Hint: The time required for the entire train to cross the pole is given. You can assume that the distance covered by a single train car in the given time will be the length of the train. Recall the speed distance time formula to solve this numerical. Ensure that all the given quantities are in the same units or in the SI units, if not then convert them before solving further.

Complete step by step solution:
The speed distance time formula states that the speed of a body is equal to the distance travelled by the body divided by the time taken by the body to travel that distance.
$Speed = \dfrac{{Distance}}{{Time}}$
The question asks us to find the length of the train when the speed of the train and the time is given.
Given that,
Speed of the running train is $v = 60km/hr$
Time taken by the train to cross the pole is $t = 9s$
But we see that the speed of the running train is not in the SI units, so we first convert it to the SI units of $m/s$ .
$v = 60\dfrac{{km}}{{hr}} = \dfrac{{60 \times 1000m}}{{60 \times 60s}}$
$ \Rightarrow v = \dfrac{{50}}{3}m/s$
Now that we have the velocity and time both in the SI units, we substitute these values in the speed distance time equation and find the length of train
$Speed = \dfrac{{Dis\tan ce}}{{Time}}$
$ \Rightarrow \dfrac{{50}}{3}m/s = \dfrac{L}{{9s}}$
$ \Rightarrow L = \dfrac{{50 \times 9}}{3}m$
$ \Rightarrow L = 150m$

Therefore, option (D) is the correct option.

Note: Make sure to convert all the quantities in their SI units or in the same units before calculations. To convert speed given in $km/hr$ to $m/s$ we multiply the given value by $\dfrac{5}{{18}}$ and get the required answer. Likewise, to convert speed given in $m/s$ to $km/hr$ we multiply the given value by $\dfrac{{18}}{5}$.
Remember that speed is the ratio of distance per time and is ignorant of the direction. Speed is a scalar quantity unlike velocity which is a vector quantity. Speed and velocity are both equal in magnitudes but velocity also has a direction.