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) = αt+ βt² and X_Q(t) =ft - t². At what time, both the buses have same velocity?

Options

• `(alpha-"f")/(1+beta)`

• `(alpha+"f")/(2(beta-1)`

• `(alpha+"f")/(2(1+beta)`

• `("f"-alpha)/(2(1+beta)`

Answer 1

`bb(("f"-alpha)/(2(1+beta))`

Explanation:

For bus P

x_p (t)  = αt + βt²

V_p (t) = α + 2βt   `[∴ "V"_"p" = ("d"x_"q")/"dt"  ]`

For bus Q

x_q(t) = ft - t²

V_q (t) = f - 2t  `[∵ "V"_"q"=("d"x_"q")/"dt"]`

As, V_p (t) = V_q(t)

⇒ α + 2βt = f - 2t

⇒ f - α = 2βt + 2t

⇒ t = `("f"-alpha)/((2beta+2))`