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The velocity of a car is plotted as shown. Determine the total distance the car moves until it stops (t = 80s). Construct the at graph.

Step-by-step

Distance Traveled: The total distance traveled can be obtained by computing the
area under the v – t graph.

s = 10(40) + \frac {1} {2} (10)(80 – 40) = 600 m

a – t Graph: The acceleration in terms of time t can be obtained by applying a = \frac { dv } { dt }. For time interval 0s \le t < 40s,

a = \frac { dv } { dt } = 0

For time interval 40s < t \le 80s, \frac { v – 10 } { t – 40 } = \frac { 0 – 10 } { 80 – 40 }, v = (- \frac { 1 } { 4 }t + 20)m/s.

a = \frac { dv } { dt } = – \frac { 1 } { 4 } = -0.250 m/{ s }^{ 2 }

For 0 \le t < 40s, a = 0.

For 40s < t \le 80, a = -0.250 m/{ s }^{ 2 }.

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