Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by x P t = α t + β t 2 and x Q t = f t - t 2 . At what time, both the buses have same velocity ?

Step-by-step solution

As we know, v = d x d t . Given, x P t = α t + β t 2 Velocity of bus P is v P = d x P d t = α + 2 β t and velocity of bus Q is v Q = f - 2 t When v P = v Q ⇒ α + 2 β t = f - 2 t ⇒ f - α = 2 β + 1 t   ⇒ t = f - α 2 β + 1