Question 594700: For the position function s(t)=-16^2+106t, complete the following table with appropriate average velocity. Then make a conjecture about the value of the instantaneous velocity at t=1
Time interval: [1,2], [1,1.5],[1,1.1],[1,1.01],[1,1.001]
Average Velocity:______,_________,______,_________,_______
Answer by dhartman0220(8)   (Show Source):
You can put this solution on YOUR website! The instantaneous velocity at any point can be found [s(t+dt)-s(t)]/dt
where dt=delta t = the increment of change that is being added to the system.
i.e. time interval (2,1)= [s(1+1)-s(1)]/1 = [s(2)-s(1)]/1
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time interval Av Velocity
(1,2) 106
(1,1.5) 106
(1,1.1) 106
(1,1.01) 106
(1,1.001) 106
at t=1 the instantaneous velocity is = to 106 because as dt aproaches 0 the av velocity = 106
evaluating the function at different time intervals (ie [2,3] [10,200]... ect)
the instantaneous velocity can be given by this equation
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IV(t)=106
deep stuff!!
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