The piecewise function that gives his velocity is graphed at the end of the answer.
A piecewise function is a function that has different definitions, depending on the input.
Between 0 and 5 minutes, the velocity increases steadily, from 0 to 35 mph, hence the function is:
v = (35/5)t
v = 7t, 0 ≤ t ≤ 5.
Between 5 and 10 minutes, the velocity remains constant at 35 mph, hence:
v = 35, 5 ≤ t ≤ 10.
At the 10 minute mark, his speed decreases to 20 mph for 2.5 minutes, hence:
m = (20 - 35)/2.5
m = -6.
v = 35 - 6(t - 10), 10 ≤ t ≤ 12.5. (considering that the velocity was at 35 mph at t = 10s).
Between 12.5 and 17.5 minutes, the velocity remains constant at 20 mph, hence:
v = 20, 12.5 ≤ t ≤ 17.5.
After 17.5 minutes until 20 minutes, the velocity decays from 20 to 0, in 2.5 minutes, hence the slope is:
m = -20/2.5 = -8.
The function is:
v = 20 - 8(t - 17.5), 17.5 ≤ t ≤ 20.
Taking these different definitions, the graph of the function is given at the end of the answer.
More can be learned about piecewise functions at https://brainly.com/question/27262465
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