Home >> Science & Nature >> Science

How to Convert Position Function to Velocity in S Domain

Mathematics is a core subject within schools and much of what is learnt is used throughout life. An application of mathematics that is commonly taught is mechanics which is the study of moving bodies. Mechanics allows the position and velocity of a particle to be described with respect to other variables such as time. This is done by using a formula known as a function. Functions can be converted to describe position or velocity with time.

Instructions

- 1
  Write down the distance as a function of time. Distance commonly has the symbol "s" and time has the symbol "t." For example, the function may be:
  
  s = 3t + 4
- 2
  Differentiate the function. When distance is a function of time, it can be converted to velocity by differentiation. This finds the rate of change of distance with time, which is the velocity. There are many different differentiation rules. The one that will be used here is:
  
  If y=x^n then dy/dx = nx^(n-1)
  
  Where dy/dx is the differentiated function.
  
  Following the example:
  
  s = 3t + 4, ds/dt = 3
  
  Hence the velocity is constant at 3 meters / second.
- 3
  Check the result by integration. Integration is the inverse function to differentiation and hence allows one to convert between velocity and position. There are many integration rules but the one that will be used here is:
  
  If y = x^n then the integral is x = ( 1 / n +1) x^(n+1)
  
  Following the example:
  
  ds/dt = 3
  
  To get back to s, integration is carried out using the above rule:
  
  s=3t + c
  
  where c=4.

Science