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Snap, [6] or jounce, [2] is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. [4] Equivalently, it is the second derivative of acceleration or the third derivative of velocity, and is defined by any of the following equivalent expressions: = ȷ = = =.
At any instant of time, the net force on a body is equal to the body's acceleration multiplied by its mass or, equivalently, the rate at which the body's momentum is changing with time. If two bodies exert forces on each other, these forces have the same magnitude but opposite directions. [1] [2]
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
Uniform or constant acceleration is a type of motion in which the velocity of an object changes by an equal amount in every equal time period. A frequently cited example of uniform acceleration is that of an object in free fall in a uniform gravitational field.
t 1 and t 2 are times when the impulse begins and ends, respectively, m is the mass of the object, v 2 is the final velocity of the object at the end of the time interval, and; v 1 is the initial velocity of the object when the time interval begins. Impulse has the same units and dimensions (MLT −1) as momentum.
For a constant mass, force equals mass times acceleration (=). For every action, there is an equal and opposite reaction. (In other words, whenever one body exerts a force F → {\displaystyle {\vec {F}}} onto a second body, (in some cases, which is standing still) the second body exerts the force − F → {\displaystyle -{\vec {F}}} back onto ...
Since the velocity of the object is the derivative of the position graph, the area under the line in the velocity vs. time graph is the displacement of the object. (Velocity is on the y-axis and time on the x-axis. Multiplying the velocity by the time, the time cancels out, and only displacement remains.)
The jump in acceleration equals the force on the mass divided by the mass. That is, each time the mass passes through a minimum or maximum displacement, the mass experiences a discontinuous acceleration, and the jerk contains a Dirac delta until the mass stops.