Answer:
(a) See attached for a graph
(b) 200 m
Step-by-step explanation:
You want a speed-time graph for a car that accelerates at 5 m/s² to a speed of 20 m/s that is maintained for 4 seconds before it decelerates to rest at a constant rate in 8 more seconds.
(a) Speed graph
The graph will have an initial slope from 0 of 5 m/s² to a maximum of 20 m/s. It will remain constant for 4 s, then will have a slope of -2.5 m/s² to reach 0 at 16 s. This is shown in the attachment.
(b) Distance
The total distance traveled is the area under the trapezoid-shaped curve. It can be found using the formula for the area of a trapezoid:
A = 1/2(b1 +b2)h
A = 1/2(4 +16)(20) = 200 . . . . . meters
The total distance traveled by the car is 200 meters.
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Additional comment
The "bases" of the trapezoid-shaped curve are the 4-second horizontal line at v = 20 m/s, and the 16-second horizontal line between the start and stop. The "height" of the trapezoid is the constant speed, 20 m/s.
Area is the product of speed (m/s) on the vertical axis, and time (s) on the horizontal axis. That product gives distance (m).
