average rates of change

[Guest]

after finding four slopes of secants (PQ1, PQ2,...) in a 'time to distance' graph of a falling object (not on earth), i was asked to determine how fast the object was going when it hit the ground (80 meters). this means i need to find it's instantaneous speed...how do i find that when x and y of the Q I want to find equals P? do i draw a tangent line? if so, how?
P=(10, 80)
Q1=(5, 20) slope=12
Q2=(7, 38) slope=14
Q3=(8.5, 57) slope=15.33
Q4=(9.5, 72) slope=16

 

[tkhunny]

This is a tough one, but only because it looks funny.

1) It is unusual to have such a problem INcrease in distance as time increases. Normally, one would START at 80, and end up at zero.

2) Aren't you missing the first point, (0,0)?

3) Where do the slopes come from? Shouldn't average slope be calculated from successive points? I get:

----- (0,0) -> (5,20) ==> (20-0)/(5-0) = 20/5 = 4
----- (5,20) -> (7,38) ==> (38-20)/(7-5) = 18/2 = 9

So, where does that leave us? Can you clarify and standardize?