Two cars `P` and `Q` start from a point at the same time in a straight line and their position are represented by `x_p(t) = at + bt^2` and `x_Q (t) = ft - t^2`. At what time do the cars have the same velocity ?

Options

A. `(a - f)/(1 + b)`
B. `(a + f)/(2 (b - 1))`
C. `(a + f)/(2 (1 + b))`
D. `(f - a)/(2 (1 + b))`

Answer

D

Explanation

`v_(P) = a + 2 bt`
`v_(Q) = f - 2t`
`v_(P) = v_(Q) rArr a + 2bt = f - 2t`
`t = (f - a)/(2 (b + 1))`