Displacement, Velocity, and Acceleration

AP Physics 1· difficulty 3/5

A runner covers the first half of a 10 km10~\text{km} run at 4 m/s4~\text{m/s} and the second half at 6 m/s6~\text{m/s}. What is the average speed for the entire run?

  • A

    10 m/s10~\text{m/s}

  • B

    5.0 m/s5.0~\text{m/s}

  • C

    5.2 m/s5.2~\text{m/s}

  • D

    4.8 m/s4.8~\text{m/s}

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Explanation

Total distance // total time: vˉ=2v1v2/(v1+v2)=2(4)(6)/(4+6)=48/10=4.8 m/s\bar v = 2 v_1 v_2 / (v_1 + v_2) = 2(4)(6)/(4+6) = 48/10 = 4.8~\text{m/s} (the harmonic-mean shortcut for equal-distance halves).

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