Tilted Forum Project Discussion Community - View Single Post - Probably really simple, I'm just not seeing it

KnifeMissile · 01-26-2004, 08:37 PM

I'm sorry, was I not clear earlier? Did my post not make any sense? Did you not read it?

Let me explain this again. The average velocity is the slope of the secant of the function during the interval in question. It is analogous to how the instantaneous velocity is the slope of the tangent at a point. Basically, the secant is a tangent during an interval instead of at a point.

So, let's examine the slope of the secant line during these intervals.

The slope of the secant is the rise divided by the run. So, if we let t be the delta time (rather than simply the variable), the formula for delta y looks like this...

Code:

delta y = y - y0
        = (40(2 + t) - 16(2 + t)^2)      - (40*2 - 16*2^2)
        =  80 + 40t  - 16(4 + 4t + t^2)  - 16
        =  80 + 40t  - 64 - 64t - 16t^2) - 16
        = -16t^2 - 24t

Since the slope of the secant is simply delta y - delta x = (-16t^2 - 24t)/t, we can just plug your numbers into this formula and it will all work out.

01-26-2004, 08:37 PM	#8 (permalink)
KnifeMissile Location: Waterloo, Ontario	I'm sorry, was I not clear earlier? Did my post not make any sense? Did you not read it? Let me explain this again. The average velocity is the slope of the secant of the function during the interval in question. It is analogous to how the instantaneous velocity is the slope of the tangent at a point. Basically, the secant is a tangent during an interval instead of at a point. So, let's examine the slope of the secant line during these intervals. The slope of the secant is the rise divided by the run. So, if we let t be the delta time (rather than simply the variable), the formula for delta y looks like this... Code: delta y = y - y0 = (40(2 + t) - 16(2 + t)^2) - (402 - 162^2) = 80 + 40t - 16(4 + 4t + t^2) - 16 = 80 + 40t - 64 - 64t - 16t^2) - 16 = -16t^2 - 24t Since the slope of the secant is simply delta y - delta x = (-16t^2 - 24t)/t, we can just plug your numbers into this formula and it will all work out. Last edited by KnifeMissile; 01-26-2004 at 10:14 PM..