# Velocity rate question

1. Nov 10, 2012

### fifaking7

1. The problem statement, all variables and given/known data
A coin is dropped from a height of 800 feet. The height, s(measured in feet), at time, t(measured in seconds is given by:

s(t)= Vit + 1/2 a t^2 + So

a) find the average velocity on the interval [1,3]
b) find the instantaneous velocity when t= 3s.
c) how long does it take the coin to hit the ground?
d) find the velocity on the interval [1,3]

2. Relevant equations
a= -32 ft/s^2
h=800 ft

3. The attempt at a solution
a) I understand that you have to derive the position function to get the velocity function but I'm having trouble doing it. To find the average though i can do f(3)-f(1)/3-1
b) I can't find it because I'm having trouble with the derivative
c &d) I do not understand it because I missed the class that my teacher went over it when i was sick

2. Nov 10, 2012

### Ray Vickson

For (a): the average is not f(3)-f(1)/3-1 (which means f(3) - [f(1)/3] - 1 exactly as you have written it). If you mean (f(3)-f(1))/(3-1) you should use parentheses.

Anyway, your expression for s(t) does not have an 'h' in it; maybe you really meant to say S0 = 800. You see, these errors start to add up and can reduce your marks!

For (b): you say you are having trouble with the derivative. Please show your work, so we can see exactly what is your source of trouble.

For (c): you need to know when s(t) = 0.

Question (d) does not make much sense as written, but maybe they want you to write a formula for velocity v(t) that applies on the interval 1 ≤ t ≤ 3.

RGV

3. Nov 10, 2012

### fifaking7

Letter d, i typed up b again. so letter D actually is below
D) find the velocity when the coin hits the ground.

My work so far

I used the 800 ft from the original statement as So instead of height

S(t)=Vi(0)t + 1/2 (-32ft/s^2)t^2 +So
S(t)= 0 -16t^2 + 800
v(t) = -32t

a) V(3)-V(1)/(3-1)
V(3) = -32(3)=-96
V(1) = -32(1)= -32

-96-(-32)/2 = -64ft/sec is my final answer

b) v(3)= -32(3)
v(3)= -96 ft/Sec is my final answer
C) I just don't understand
D)I know i need C but don't understand it