The engineer of a passenger train traveling at 25.0 m/s sights a freight train whose caboose is 200 m ahead on the same track. The freight train is traveling at 15.0 m/s in the same direction as the passenger train. The engineer of the passenger train immediately applies the brakes, causing a constant acceleration of 0.100 m/s2 in a direction opposite to the train’s velocity, while the freight train continues with constant speed.  Take x = 0 at the location of the front of the passenger train when the engineer applies the brakes.  (a) If t = 0 is the instant when the engineer applies the brakes, at what later time will there be a collision?  (b) Where will the collision take place?  (c) On a single graph, sketch the position of the front of the passenger train and the back of the freight train.

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Relative Velocity

It is a measurement of an object with regards to the other object which is moving or stable or stationary. For example, if we are traveling in a bus and the bus is moving at speed of 50km/hr, then our speed is according to the nearby passenger on the bus is zero. According to them, we are not moving. But if one person standing on the ground or road observes us from outside of the bus, according to him we are moving at a speed of 50km/hr and the bus is also moving at a speed of 50km/hr. Now, the motion is recognized by the observer, it depends on a frame of reference or observer. This is motion called relative motion.