calculating average velocity

Question

anonymous · Answer

When a ball is thrown vertically upward into the air with a velocity of 56 ft/sec its height, y(t), in feet after t seconds is given by $$y(t)=56t-16t ^{2}$$ Find the average velocity of the ball over the interval from 3 to 3+h seconds, $$h \neq0$$

anonymous · Answer

answer choices:
1. average vel. = −(41 + 16h) ft/sec
2. average vel. = −(40 − h) ft/sec 
3. average vel. = −(41 − 16h) ft/sec 
4. average vel. = −(41 + h) ft/sec 
5. average vel. = −(40 + 16h) ft/sec 
6. average vel. = −(40 − 16h) ft/sec

ganeshie8 · Answer

average velocity =  $\large   \frac{y(3+h) - y(3)}{(3+h) - h}$

ganeshie8 · Answer

simplify

anonymous · Answer

@ganeshie8 I got -(40+16h) ft/sec

anonymous · Answer

Now..how do I find the instantaneous velocity of the ball after 3 seconds?

ganeshie8 · Answer

Excellent ! thats correct

ganeshie8 · Answer

familiar wid calculus ?

anonymous · Answer

haha I am taking calculus.

anonymous · Answer

would I substitute t for 3 from the answer I got from the first problem?

anonymous · Answer

wait..no that's not rigt.

ganeshie8 · Answer

no, that just gives u height

anonymous · Answer

oh i see. what do I do, now?

ganeshie8 · Answer

did u get how the average velocity was found ?

ganeshie8 · Answer

Average velocity =  $\large   \frac{y(3+h) - y(3)}{(3+h) - h}$

u can use the same formula for instantaneous velocity, but u need to MAKE THE h SOOO SMALL

ganeshie8 · Answer

then oly, u wil get the velocoty right after 3 seconds. getting ?

anonymous · Answer

yeah I understood that formula

anonymous · Answer

that's what I used earlier

ganeshie8 · Answer

make h=0.001 and see wat u wud get

anonymous · Answer

Do i need to plug in a 3 anywhere?

ganeshie8 · Answer

3 is already there in the formula, just put h value and simplify

anonymous · Answer

I seee. thank  you!

ganeshie8 · Answer

wait a sec, you have already simplifies the average velocity

average velocity between 3 & h seconds =  -(40+16h) ft/sec

ganeshie8 · Answer

right ?, now simply put h = 0.001 above. you will get instantaneous velocity at time 3

ganeshie8 · Answer

that wud be oly the APPROXIMATE value

anonymous · Answer

wait. what if I just plug in 3 into $$56t-16t ^{2}$$

anonymous · Answer

@ganeshie8

anonymous · Answer

@ganeshie8 is the answer -40?

ganeshie8 · Answer

yes thats right