The graph below shows the total distance s, in miles, traveled by a bicyclist af

Question

The graph below shows the total distance s, in miles, traveled by a bicyclist after t hours.

(a) Estimate the bicyclist's average velocity over the following time intervals.
Over [0,1], the average velocity is approximately ? mi/hr.
Over [1,2.5], the average velocity is approximately ?mi/hr.
Over [2.5,3.5], the average velocity is approximately ? mi/hr.

(b) Estimate the bicyclist's instantaneous velocity at the following times.
At t=1/2 hour, the instantaneous velocity is approximately ?mi/hr.
At t=2 hours, the instantaneous velocity is approximately ? mi/hr.
At t=3 hours, the instantaneous velocity is approximately ? 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 ? hr.

Explanation / Answer

a) Average velocity is defined by:
Vavg = (xf-xi)/delta_t, hence,
Over [0,1], Vavg = (15-0)/1 = 15 mi/hr
Over [1,2.5], Vavg = (20-15)/1.5 = 3.33 mi/hr
Over [2.5,3.5], Vavg = (40-20)/1 = 20 mi/hr
b) Instantaneous velocity is the slope of x-t curve at that instant of time.
At t=0.5 hr, V = 15 mi/hr
At t= 2 hr, V = 0 mi/hr
At t = 3 hr, V = 20 mi/hr
c) The velocity is maximum where slop of the curve is maximum.
Maximum velocity = 20mi/hr at time t = 3 hr.

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