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

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Accepted Answer

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

[latex]s = 10(40) + \frac {1} {2} (10)(80 - 40) = 600 m[/latex]

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

[latex]a = \frac { dv } { dt } = 0[/latex]

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

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

For [latex]0 \le t < 40s, a = 0[/latex].

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

Question : The velocity of a car is plotted as shown. Determine the tot...

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