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Representing Motion

AP Physics 1· difficulty 3/5

An object's position is given by x(t)=2+6t−t2x(t) = 2 + 6t - t^2 (SI units). At t=2 st = 2~\text{s}, what is the object's instantaneous velocity?

  • A

    6 m/s6~\text{m/s}

  • B

    0 m/s0~\text{m/s}

  • C

    4 m/s4~\text{m/s}

  • D

    2 m/s2~\text{m/s}

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Explanation

v(t)=dx/dt=6−2tv(t) = dx/dt = 6 - 2t. At t=2t = 2, v=6−4=2 m/sv = 6 - 4 = 2~\text{m/s}. (Without calculus, recognize uniform acceleration a=−2 m/s2a = -2~\text{m/s}^2 and v0=6 m/sv_0 = 6~\text{m/s}: v=6+(−2)(2)=2v = 6 + (-2)(2) = 2.)

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