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Wize University Dynamics Textbook (Master) > Transition to Dynamics

Dynamics Fundamentals

IntroductionPrevious Section
Review of Useful Trigonometric Equations & Laws of Sin & Cos Next Section
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In dynamics, there are 3 variables we are generally interested in knowing:
  • Displacement/Position
  • Velocity/Speed
  • Acceleration

Those variables are related as follows:

v=dxdtv = \frac{dx}{dt}

a=dvdt=d2xdt2a = \frac{dv}{dt} = \frac{d^2x}{dt^2}

We sometimes use a dot above a variable to show its derivative with respect to time

v=x˙v = \dot{x}

a=v˙=x¨a = \dot{v} = \ddot{x}

Note that displacement is a vector quantity, while distance is a scalar quantity. Similarly, velocity is a vector while speed is a scalar.

By using the chain rule, we can show that:

a=dvdt=dxdtdvdx=vdvdxa = \frac{dv}{dt} = \frac{dx}{dt}\frac{dv}{dx}=v\frac{dv}{dx}