NSW Y11 Maths - Extension 1 Rates of Change Rates Of Change (Time)

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Rates Of Change (Time) Theory

NSW Syllabus Reference

NSW Syllabus Reference: ME-C1.1: Rates of change with respect to time. This will require student toย 

  • describe the rate of change of a physical quantity with respect to time as a derivative
  • find and interpret the derivative \(\dfrac{dQ}{dt}\) given a function in the form \(๐‘„ = ๐‘“(๐‘ก)\), for the amount of a physical quantity present at time \(t\)
  • describe the rate of change with respect to time of the displacement of a particle moving along the \(๐‘ฅ\)-axis as a derivative \(\dfrac{dx}{dt}\) or \(\dot{x}\)
  • describe the rate of change with respect to time of the velocity of a particle moving along the \(๐‘ฅ\)-axis as a derivative \(\dfrac{d^2x}{dt^2}\) or \(\ddot{x}\)

Ref:ย https://educationstandards.nsw.edu.au/

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  • Rates Of Change (Time) - Video - Rate of Change of Volume with Time Derivatives Application AP

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Theory

The rate of change of a function is the derivative of that function.

If a real-life situation is expressed as a function of time, then the rate of change is the derivative of that function.

For example \(V = f(t)\) if is the volume of a tank at time \(t\) minutes then \(\dfrac{{dV}}{{dt}}\) is the rate at which the fluid flows out of the tank.