Newton's Second Law [The Physics Travel Guide]

--- equations:newtons_second_law [2018/05/13 09:18]
jakobadmin ↷ Links adapted because of a move operation
+++ equations:newtons_second_law [2018/12/15 12:01] (current)
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-**Boundary Conditions**
+**Boundary or Initial Conditions**
-Since Newton's second law contains the second derivative of the location: $\vec a = \frac{\partial^2 r}{\partial t^2}$, we need two boundary conditions to solve it. (In technical terms, we say that Newton's law is a second order differential equation.) For example, we can use the location of the object at the starting time and the velocity at the starting time as boundary conditions. Alternatively, we could use, for example, the location of the object at two different points in time as boundary conditions.
+Since Newton's second law contains the second derivative of the location: $\vec a = \frac{\partial^2 r}{\partial t^2}$, we need two boundary conditions to solve it. Whenever the independent variable is time, //boundary// conditions are usually called //initial// conditions. (In technical terms, we say that Newton's law is a second order differential equation.) For example, we can use the location of the object at the starting time and the velocity at the starting time as boundary conditions. Alternatively, we could use, for example, the location of the object at two different points in time as boundary conditions.