Instantaneous Velocity of a particle

[AcidicVision]

Homework Statement

The position of a particle as a function of time is given by x = ( -2.00 m/s)t + ( 3.00 m/s^3)t^3. (a) Plot x versus t for time from t = 0 to t = 1.00 s. (b) Find the average velocity of the particle from t = 0.150s. to t = 0.250s. (c) find the average velocity from t = 0.190 s. to t = 0.210 s. (d) Do you expect the instantaneous velocity at t = 0.200 s. to be closer to -1.62 m/s, -1.64 m/s, or -1.66 m/s? Explain.

Homework Equations

The Attempt at a Solution

Ok, I have no idea where to even begin. The book I am using is College Physics by: James S. Walker. And section 2-3 Instantaneous Velocity is barely a page and a half long and has nothing in the text, example or conceptual excercises that even resembles this.

Im not looking for someone to provide the solutions, but direction and maybe some explanation as to why I need to do what. Ill be watching this thread so I can be prompt with responces to anyone willing to assist me. Ill also give out my gmail and aim for more direct chat for help if someone is up for it.

Thanks a lot.

 

[Andrusko]

Part a is just a graph. Factorize $$x(t)$$ and solve for the roots (when x(t) = 0) and find the y-intercept (solve x(t) for t=0).

$$v_{avg} = \frac{\Delta x}{\Delta t} = \frac{x_{final} - x_{initial}}{t_{final} - t_{initial}}$$

Have a crack at part b with that. If you can't get it, I'll give you another hint.

Part c is just like part b.

Part d... investigate that when you have done part b and c.