What Is the Difference Between Average and Instantaneous Velocity?

[phragg]

A position-time graph for a particle moving along the x-axis is shown below:

(a) Find the average velocity in the time interval t = 1.50 s to t = 4.00 s.
(b) Determine the instantaneous velocity at t = 2.00 s by measuring the slope of the tangent line shown in the graph.
(c) At what value of t is the velocity zero?

http://img241.imageshack.us/img241/1514/tangetsb6.jpg

I figured that (a) was the easy part as I went ahead to solving that
$$v_{ave} = \frac{\Delta x}{\Delta t}$$

$$\Delta t = t_f - t_i$$
$$\Delta t = 4.00 s - 1.50s$$
$$\Delta t = 2.50 s$$

$$\Delta x = x_f - x_i$$
$$\Delta x = 2m - 7m$$
$$\Delta x = -5m$$

$$v_{ave} = \frac{-5m}{2.50s}$$
$$v_{ave} = -2m/s$$

So after that was done I went on to part (b) which first asked to find the slope of the tangent point was easily done by:

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$
$$m = \frac{0 - 12}{4 - 0}$$
$$m = \frac{-3}{1}$$

Now I am completely stumped as to what they're asking for how to Determine the instantaneous Velocity at t = 2.00 s and Don't get me started on (c). Oh an p.s. Hey I'm new to PF ;p!

 

[CompuChip]

Hi, welcome to PF.
Actually, you already solved b :)
The key thing you are missing, is that instantaneous velocity at some time is the slope of the (t, x) graph at that point.

This should also help you solve c.