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Calculation of the speed difference for a uniform acceleration. 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.
In terms of a displacement-time (x vs. t) graph, the instantaneous velocity (or, simply, velocity) can be thought of as the slope of the tangent line to the curve at any point, and the average velocity as the slope of the secant line between two points with t coordinates equal to the boundaries of the time period for the average velocity.
This slope therefore defines the average acceleration over the interval, and reducing the interval infinitesimally gives , the instantaneous acceleration at time , or the derivative of the velocity with respect to time (or the second derivative of the position with respect to time).
In contrast to an average velocity, referring to the overall motion in a finite time interval, the instantaneous velocity of an object describes the state of motion at a specific point in time. It is defined by letting the length of the time interval Δ t {\displaystyle \Delta t} tend to zero, that is, the velocity is the time derivative of the ...
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.
Average speed does not describe the speed variations that may have taken place during shorter time intervals (as it is the entire distance covered divided by the total time of travel), and so average speed is often quite different from a value of instantaneous speed. [3] If the average speed and the time of travel are known, the distance ...
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An elastically deformable mass deforms under an applied force (or acceleration); the deformation is a function of its stiffness and the magnitude of the force. If the change in force is slow, the jerk is small, and the propagation of deformation is considered