"There are two types of information that one normally wishes to find from a velocity versus time graph. The first and simplest objective is finding the acceleration. The second is to find a position versus time graph that produced the velocity versus time graph.
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From a Japanese TV show - a real life example of adding vectors and relative motion. The truck is moving at 100km/hr and a ball is shot backwards at 100 km/hr, resulting in it coming to a complete stop.