1. Average of a function.

The height at time t of a small weight oscillating at the end of a spring is .5cos(8t).

How can I find the average velocity over the time intervals [3,4], [3,3.5], [3,3.1]?

How can i find the weights instantaneous velocity at time t = 3?

2. Originally Posted by colerelm1
The height at time t of a small weight oscillating at the end of a spring is .5cos(8t).

How can I find the average velocity over the time intervals [3,4], [3,3.5], [3,3.1]?

How can i find the weights instantaneous velocity at time t = 3?
You're expected to know and apply the following:

The average rate of change of a function f(x) over the interval [a, b] is given by $\displaystyle \displaystyle \frac{f(b) - f(a)}{b - a}$

The instantaneous rate of change of a function at x = a is $\displaystyle f'(a)$ where $\displaystyle f'(x)$ is the derivative of the function.

3. avg velocity = displacement/time taken.
so over the interval [3,4] avg velocity = (0.5cos(8*4)-0.5cos(8*3))/(4-3). rest can be done in the same way.

for instantaneous velocity just differentiate the function 0.5cos(8t). put t=3 in the derived function.