Question

If a rock is thrown upward on the planet Mars with a velocity of 7 m/s, its height in meters t seconds later is given by y = 7t − 1.86t2. (Round your answers to two decimal places.)
(a) Find the average velocity over the given time intervals.
(i) [1, 2]
(ii) [1, 1.5]
(iii)[1, 1.1]
(iv) [1, 1.01]
(v) [1, 1.001]

(b) Estimate the instantaneous velocity when t = 1.

Answer 1

the equation is y= 7t-1.86t^2

Answer 2

To get the average velocity (m/s), on the interval [a,b] just calculate [y(b)-y(a)]/(b-a) -- in other words, how far it moved (distance), divided by how long it took (time)

I figure you can probably do that. You are, after all, taking calculus, so your algebra I should be OK.

The results in steps i-v should show a sequence converging on y'(1) where

y'(t) = 7 - 3.72t
y'(1) = 3.28