Average velocity question? [duplicate]

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I usually know how to do these but this one gives me trouble.

If a ball is thrown into the air with a velocity of 46 ft/s, its height in feet t seconds later is given by $y = 46t − 16t_{2}$.

(a) Find the average velocity for the time period beginning when t = 2 and lasting for each of the following. .5 seconds ______ .1 seconds ______ .05 seconds _______ .01 seconds ______

(b) Estimate the instantaneous velocity when $t = 2$.

_______ ft/s

marked as duplicate by user147263, user296602, N. F. Taussig, colormegone, Rory DaultonJan 30 '16 at 23:45

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• Such questions are all the same and have all been asked and answered before. Just search. – user147263 Jan 30 '16 at 21:49
• If you ever need to ask future questions here is meta.math.stackexchange.com/questions/5020/… for properly displaying numbers, variables, etc. – Arbuja Jan 30 '16 at 21:51
• Also please note this is not a site where you can simply put down a questions and expect us to do all the work for you. Please show how you attempted to solve the problem. – Arbuja Jan 30 '16 at 21:56
• Just how is this problem giving you trouble? – Rory Daulton Jan 30 '16 at 23:45

1 Answer

You have height $h$ as a function of time $h=f(t)$

The rate of change of height is the velocity so take the derivative of height with respect to time to get a function for velocity $v$.

To get the average of $v$ from time $t=2$ to a final time $t=T$ use the integral

$\frac{1}{T-2}\int_{2}^{T}v dt$