## Question:

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