Question

A ball is dropped from a tower 350 meters above the ground with position function s(t) = 4.9t2+ 350.

What is the velocity of the ball after 2 seconds?

Include units in your answer.

Answer 1

Do you first find the derivative?

Answer 2

yes

Answer 3

So 9.8t

Answer 4

yes, v(t) = d/dt s(t)

Answer 5

Then plug 2 in for t?

Answer 6

yep

Answer 7

right

Answer 8

19.6 m/s

Answer 9

yes

Answer 10

Awesome, thank you. Mind making sure I'm correct on another one? I think I know how to do them, I'm just checking..

Answer 11

ok

Answer 12

Thank you... The cost in dollars of producing x units of a particular brand of notebook is C(x) = x2 – 400.

Find the average rate of change of C with respect to x when the production level is changed from x = 100 to x = 102. Include units in your answer.
Find the instantaneous rate of change of C with respect to x when x = 100. Include units in your answer.

Answer 13

So for A, you plug 102 in, and the 100. Subtract (c(102) - c(100)) then divide by 102-100

Answer 14

exactly

Answer 15

Then for B, you find the derivative and plug 100 in?

Answer 16

and for the second part you differentiate C(x) with respect to x

Answer 17

right

Answer 18

What would be the units? It doesn't really tell you what you are looking for

Answer 19

cost per units produced

dollars per notebook

Answer 20

Oh, thank you!

Answer 21

yw