Practice question · Numerical answer
Newton's second law written as F = m times the second derivative of x with respect to t is a differential equation. What is its order?
Hints
- The order of a differential equation is the highest derivative that appears in it.
- Acceleration is the second derivative of position.
Show the answer
2
Why
The highest derivative is the second, so the equation is second order, which is exactly why two initial conditions ( and ) are needed to pick out a unique trajectory. Order and number of required initial conditions always match.
Practise Mathematical Methods in Physics
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