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Physics Question on Motion in a plane

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) = ft – t 2. At what time, both the buses have same velocity?

A

α−f1+β\frac{α-f}{1+β}

B

α−f2(β+1)\frac{α-f}{2(β+1)}

C

α−f2(1+β)\frac{α-f}{2(1+β)}

D

f−α2(1+β)\frac{f-α}{2(1+β)}

Answer

α−f1+β\frac{α-f}{1+β}

Explanation

Solution

The correct option is(D): f−α2(1+β)\frac{f-α}{2(1+β)}

X P = α t + β t 2

X Q = ft – t 2

∴ V P = α + 2β t

V Q = f – 2 t

∵ V P = V Q

⇒ α + 2β t = f – 2 t

_⇒ _t=f−α2(1+β)t=\frac{f-α}{2(1+β)}.