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Conservation of Energy

AP Physics 1· difficulty 3/5

A B C h=20 m h=12 m h=2 m

A cart starts at rest at point A (h=20 mh = 20~\text{m}) on a frictionless track. Using g≈10 m/s2g \approx 10~\text{m/s}^2, what is the cart's speed at point C (h=2 mh = 2~\text{m})?

  • A

    18 m/s18~\text{m/s}

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  • B

    20 m/s20~\text{m/s}

  • C

    14 m/s14~\text{m/s}

  • D

    24 m/s24~\text{m/s}

Explanation

Energy conservation: 12v2=g(hA−hC)=10(20−2)=180\tfrac{1}{2}v^2 = g(h_A - h_C) = 10(20 - 2) = 180, so v=360≈19 m/sv = \sqrt{360} \approx 19~\text{m/s}, closest to 18 m/s18~\text{m/s}.

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