Position, Velocity, and Acceleration using Integrals

AP Calculus AB· difficulty 3/5

A particle has v(t)=3tv(t) = 3 - t on [0,5][0, 5]. Total distance traveled?

  • A

    5/25/2

  • B

    55

  • C

    25/225/2

  • D

    13/213/2

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Explanation

Distance: 03(3t)dt+35(t3)dt=9/2+2=13/2\int_0^3 (3-t)\,dt + \int_3^5 (t-3)\,dt = 9/2 + 2 = 13/2.

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