Problem

A car moving at 95 km/h passes a 1.00-km-long train traveling in the same direction on a track that is parallel to the road. If the speed of the train is 75 km/h, how long does it take the car to pass the train, and how far will the car have traveled in this time? What are the results if the car and train are instead traveling in opposite directions?

Problem 59 GP

Step-by-step solution

Step 1 of 6</p>

Following is the schematic of the kinematic situation that is described in the problem.

Step 2 of 6</p>

APPROACH:

Here the car and train passing each other with a constant speed of 95 km/h and 75 km/h with respect to the ground. We want to determine the time taken by the car to pass the train which can be calculated by dividing the length of the train by the relative speed between them. The distance traveled by car while passing the train can be calculated by multiplying the speed of the car with respect to the ground with the time taken to pass the train.

Step 3 of 6</p>

Consider a reference frame in which the train is at rest. Then, relative to the train, the car is moving with 20 km/h. The car has to travel 1.0 km in that frame to pass the train, and so the time required to pass the train can be found by calculating the relative speed first.

Relative speed

Distance to be traveled = 1km

Therefore, time taken by car