t(secs) | 0.999 | 1 | 1.001 |
x(feet) | 84.026984 | 84.000000 | 83.972984 |
f:= t -> 95 + 5*t - 16*t^2;and then calculating average velocities over short intervals which begin or end at t=2:
(f(2.01) - f(2))/ (2.01-2);
(f(2)-f(1.99))/(2-1.99);and so forth. What value would you assign for the instantaneous velocity at t=2?
vav := t -> (f(t+h)-f(t))/h;This will give the average velocity over the time interval [t,t+h] once we have assigned a value to h. Do part (a) again using vav. Then use vav to find the instantaneous velocity at several (at least three) other values of t.
plot({f(t),vav(t)},t=0..2.6)Do this several times with decreasing values of h (but only turn in \it one plot). What do the graphs of all the 'vav' s have in common? How do they differ? How is the graph of f(t) related to that of vav(t) . In particular how does f behave when vav is positive? negative? big? small? -- Is this behavior precise or only approximate?