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Two cars P and Q start from a point at t...

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 ?

A

`(a-f)/(1+b)`

B

`(a+f)/(2(b-1))`

C

`(a+f)/(2(1+b))`

D

`(f-a)/(2(1+b))`

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • Two cars P and Q start from a point at the same time in a straight line and their positions 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 ?

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

  • The position of a particle moving on a straight line depends on time t as x=(t+3)sin (2t)

    A
    Its velocity at the initial moment is 6 m/s
    B
    Its acceleration at the initial is `-8 m//s^(2)`
    C
    It has velocity of 3 m/s at `t=(pi)/2` sec
    D
    It has an acceleration of `2 m//s^(2)` at `t=(pi)/4` sec

  • Position - time graph for a particle is shown in figure. Starting from t = 0, at what time t, the average velocity is zer?

    A
    1 s
    B
    3 s
    C
    6 s
    D
    7 s
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