Representing Motion

AP Physics 1· difficulty 4/5

20 4 12 16 t

The graph shows velocity (m/s) vs. time (s): the object accelerates from 0 to 20 m/s in 4 s, holds steady until 12 s, then decelerates to 0 at 16 s. What total distance does it travel?

  • A

    200 m

  • B

    320 m

  • C

    160 m

  • D

    240 m

    check_circle

Explanation

Distance equals the area under the v-t curve. The shape is a trapezoid with the two parallel sides being the top (8 s of cruise from 4 to 12 s) and the bottom (the full 16 s baseline), at height 20 m/s. Area =12(b1+b2)h=12(8+16)(20)=240= \tfrac{1}{2}(b_1 + b_2)\cdot h = \tfrac{1}{2}(8 + 16)(20) = 240 m.

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