1. ## Instantaneous Velocity

Given (1,19) (2,33) (3,74); Estimate the inst. velocity when t=2 by averaging the average velocities for the periods [1,2] and [2,3]

I would use v=d/t right? but how exactly does the averaging work? Would I find v for each coordinate, then average it with the specified other in brackets, and then average those? Or would I average the coordinates within the brackets, then find v for the "new" coordinate, then average the brackets together? Am I reading too far into this?

2. The first set of points you have are (t, f(t)), so for each interval you would have to find the arc lenght betweem the points (1,19) and (2,23), and then for (2,23) and the other, and average them to get an aproximation of v when t=2.
I hope I'm right.
The concern i have is that you don't have an function.

3. what was the equation for arc length?

and all they gave me was a table with the coordinates

4. Originally Posted by MaryLou
Given (1,19) (2,33) (3,74); Estimate the inst. velocity when t=2 by averaging the average velocities for the periods [1,2] and [2,3]

I would use v=d/t right? but how exactly does the averaging work? Would I find v for each coordinate, then average it with the specified other in brackets, and then average those? Or would I average the coordinates within the brackets, then find v for the "new" coordinate, then average the brackets together? Am I reading too far into this?
Are those meant to be coordinates from an x versus t graph? $v_{\text{avarage}} = \frac{\Delta x}{\Delta t} = \frac{x_2 - x_1}{t_2 - t_1}$.

I doubt very much you're expected to calculate arclengths.

5. its a table where t (seconds) would be the independent and s (feet) would be dependent; (t,s)

6. Originally Posted by MaryLou
its a table where t (seconds) would be the independent and s (feet) would be dependent; (t,s)
Then replace x with s in my first reply, substitute the data and do the calculations.

7. okay, perfect! thanks