KINEMATICS II
1. The concept of the derivative of the function is exceptionally important. The derivative shows that how fast the function changes when its argument is changed. (Remember that for f ( x) we say that f is a function that depends upon the argument x. You should think of f as a machine which gives you the value f when you input x.)
2. Functions do not always have to be written as f ( x). us where a body is at different times t.
3. The derivative of x(t ) at time t can be defined as:
4. Now let's see how to calculate the derivative of a simple function such as x(t ) = t 2 . We should first calculate the difference in x at two slightly different values say, t and t + Δt, while that recall we choose Δt to be extremely small:
5. In exactly the same manner you can show that if x(t ) = t n then:
This is an exceptionally useful result.