(1 point) The graph below shows the total distance s, in miles, traveled by a bi

Question

(1 point) The graph below shows the total distance s, in miles, traveled by a bicyclist after t hours. 40mi distanoe 35mi 30 mi 25mi 20mi 10 mi 5mi mi ti me Dhr 0.5hr 1hr 15ht 2hr 2.5h 3 ht 3.5hr 4ht (a) Estimate the bicyclist's average velocity over the following time intervals. Over [0,1. the average velocity is approximately 15 Over 1,2.5). the average velocity is approximately Over [2.5, 3.5, the average velocity is approximately mi/hr mi/hr m/hr (b) Estimate the bicyclist's instantaneous velocity at the foll At t 1/2 hour, the instantaneous velocity is approximately At t 2 hours, the instantaneous velocity is approximately At 3 hours, the instantaneous velocity is approximately 30 times mi/hr mi/hr. mi/hr (c) Estimate the bicyclist's maximum velocity and the specific time at which it occurs The maximum velocity is approximately mi/hr, which occurs when t

Explanation / Answer

a) Average velocity over 0 to 1

v = (15-0)/1 = 15 mi/hr

over 1 to 2.5

v = (21-15)/(2.5 -1) = 6/1.5

v= 4 mi/hr

over 2.5 t0 3.5

v = (39-21)/(3.5-2.5) = 18/1

v = 18 mi /hr

b) at 1/2 hr

the instantanious velocity is almost constant from 0 to 1/2 hr

so the instantanious velocity v =(9-0)/0.5 = 18 mi/hr

at 2 hr

the slope is zero

so instantanious velocity is 0

at 3 hrs

2.8 hrs to 3.2 hrs velocity is almost constant

so v = (35 -25)/(3.2 -2.8) = 10/0.4

v = 25 mi/hr

c) maximum velocity is 25mi/hr and occurs between 2.8 hrs to 3.2 hrs

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