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Representing Motion

AP Physics 1· difficulty 3/5

0 2 5 7 0 10 t (s) v (m/s)

An object's velocity ramps from 00 to 10 m/s10~\text{m/s} over 2 s2~\text{s}, stays at 10 m/s10~\text{m/s} for 3 s3~\text{s}, then ramps down to 00 over the next 2 s2~\text{s}. What is the total displacement?

  • A

    35 m35~\text{m}

  • B

    70 m70~\text{m}

  • C

    50 m50~\text{m}

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  • D

    100 m100~\text{m}

Explanation

Area under vv-vs-tt: 12(2)(10)+(3)(10)+12(2)(10)=10+30+10=50 m\tfrac{1}{2}(2)(10) + (3)(10) + \tfrac{1}{2}(2)(10) = 10 + 30 + 10 = 50~\text{m}.

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