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Time at which two cars with positions at + bt^2 and Ft - t^2 have the same velocity

The same question, asked 2 times: 11 May 2023 S2, 11 May 2024 S2. Every wording below, oldest first.

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  1. Question 1

    11 May 2023 S2

    48
    Two cars start from a point at the same time in a straight line and their positions are represented by x1(t)=at+bt2x_1(t) = at+bt^2 and x2(t)=Ft−t2x_2(t) = Ft-t^2. At what time do the cars have the same velocity?

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  2. Question 2

    11 May 2024 S2

    38
    Two cars A and B start from a point at the same time in a straight line and their positions are represented by RA(t)=at+bt2R_A(t) = at + bt^2 and RB(t)=xt−t2R_B(t) = xt - t^2. At what time do the cars have same velocity?

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