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 ?

Question

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 = &#945; t + &#946; t 2 and x Q t = f t - t 2 . At what time, both the buses have same velocity ?

Aicharya · Accepted Answer

As we know, v = d x d t . Given, x P t = &#945; t + &#946; t 2 Velocity of bus P is v P = d x P d t = &#945; + 2 &#946; t and velocity of bus Q is v Q = f - 2 t When v P = v Q &#8658; &#945; + 2 &#946; t = f - 2 t &#8658; f - &#945; = 2 &#946; + 1 t &#160; &#8658; t = f - &#945; 2 &#946; + 1

Two buses P and Q start from a point at the same time and move in a straight line and their positions are…

Solution