Question

Two trains 121 m and 99 m in length are running in opposite directions with velocities ${\text{40km}}{{\text{h}}^{{\text{ - 1}}}}$ and ${\text{32km}}{{\text{h}}^{{\text{ - 1}}}}$. In what time will they completely cross each other?
(A) 9s
(B) 11s
(C) 13s
(D) 15s

Answer 1

This could be simply solved by breaking the total distance into two parts and applying the basic formula of time. The average speed is the distance per time ratio.
Formula used: Here, we will use the basic formula of speed, distance and time:
${\text{T = }}\dfrac{{\text{D}}}{{\text{V}}}$
Here, ${\text{V}}$ is the mean speed of the car
${\text{D}}$ is the total distance travel
$T$ is the travel time

Complete step by step answer:
We will start by considering the total distance to be${\text{t}}$,
On converting Km/hr to m/s:
${\text{v = 72km/hr = 72 \times }}\dfrac{{\text{5}}}{{{\text{18}}}}{\text{ = 20m/s}}$
Similarly, the distance to be travelled:
${\text{D = }}\left( {{\text{121 + 99}}} \right){\text{m = 220m}}$
Now the time taken:
${\text{t = }}\dfrac{{\text{D}}}{{\text{V}}}{\text{ = }}\dfrac{{{\text{220}}}}{{{\text{20}}}}{\text{ = 11sec}}$
Thus, the time taken to travel the entire distance is 11 sec.

The correct option is B.

Additional Information : Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance. The first scientist to measure speed as distance over time was Galileo. Time in physics is defined by its measurement: time is what a clock reads. In classical, non-relativistic physics, it is a scalar quantity and, like length, mass, and charge, is usually described as a fundamental quantity.

Note: It should always be kept in mind that there is a difference between speed and velocity. Just as distance and displacement have distinctly different meanings, same is the situation between speed and velocity. Velocity is a vector quantity that refers to the rate at which an object changes its position whereas speed is a scalar quantity that refers to how fast an object is moving. Velocity gives us a sense of direction whereas speed does not give any sense of direction.