Sunday, 15 June 2014

Differentiation - Rate of change

What is rate of change?
It refers to the change of a physical quantity with time. One good example is speed. 
Speed is the change in distance per unit time. If we let distance be s, and let time be t. In Mathematical terms, the rate of change of s with respect to t can be written as:

What is the units of ds/dt? Since distance, s, has a unit of metre, and time, t, has a unit of seconds, then ds/dt has units of m/s.

Chain Rule

If you know the rate of change of x with time (dx/dt),and need to find the rate of change of V with time (dV/dt), you need an equation with V and x, and subsequently differentiate it to find dV/dx. Using the following equation, dV/dt can be found. 

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