A train is running at a speed of $86\text{ km/h}$ on a straight railway track and a small car on a parallel road is running at a speed of $40\text{ km/h}$. How long (in s) will the train take to cross the car completely if the train is $490\text{ m}$ long and they are running in opposite directions?

To find the time taken by the train to cross the car, we use the concept of relative speed.Given:Speed of the train ($S_1$) = $86\text{ km/h}$ Speed of the car ($S_2$) = $40\text{ km/h}$ Length of the train ($L$) = $490\text{ m}$ (Since the car is small, its length is negligible).Direction = Opposite directionsWhen two objects move in opposite directions, their relative speed ($S_{\text{rel}}$) is the sum of their individual speeds:
$$S_{\text{rel}}=S_1+S_2=86+40=126\text{ km/h}$$
Convert the relative speed from $\text{km/h}$ to $\text{m/s}$:
$$S_{\text{rel}}=126\times \frac{5}{18}=7\times 5=35\text{ m/s}$$
The distance to be covered to cross the car completely is equal to the length of the train:
$$\text{Distance}=490\text{ m}$$
The time taken ($t$) is given by:
$$t=\frac{\text{Distance}}{S_{\text{rel}}}=\frac{490}{35}=14\text{ s}$$