Post #19

Average Speed

First of all, remember that a slope is the y value, or dy, of a derivative.

Example:

A ball is flung from a little child. It's path is projected as y=4.9t2m in "t" seconds. What is the average speed of the ball from 0 to 3 seconds?

1. Set up equations and intervals: (f(b)-f(a))/(b-a) 4.9t^2 [0,3]


2. Plug in a and b values for t: f(b)=4.9(3)2=44.1 f(a)=4.9(0)2=0

3. Plug into main equation and solve: (44.1-0)/(3-0)=14.7m/s

Average speed is used for many different things, from finding the speed at which a cannonball was launched out of a cannon from how fast a cheetah runs in a straight line trying to catch it's prey. The concept behind average speed is a fairly simple concept that many people understand right away. You're basically finding the slope of the equation using calculus and algebra. If I ask someone what the average speed of a ball from [3,4] if it's path was graphed as y=x.

y=(4) y=(3) (4-3)/(4-3)=1

First Derivative Test:

1. Take the derivative of the original problem.
2. Set the first derivative equal to Zero.
3. Solve for x.
4. Create intervals for x. i.e. (-∞, 1) (1, 4) (4, ∞)
5. Pick a number in the intervals then plug that number in the first derivative for x.
6. Solve.