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

Answer

D

Explanation

`v_(P)=(dx_(P))/(dt)=a+2bt`
`V_(Q)=(dx_(Q))/(dt)=f-2t`
`v_(P)=v_(Q)impliesa+2bt=f-2t`
`t=(f-a)/(2(b+1))`