# Velocity (avg/instantaneous)

1. Sep 9, 2008

### 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 [Broken]

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!

Last edited by a moderator: May 3, 2017
2. Sep 9, 2008

### 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.