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Galileo's demonstration of the law of the space traversed in case of uniformly varied motion. It is the same demonstration that Oresme had made centuries earlier. The mean speed theorem , also known as the Merton rule of uniform acceleration , [ 1 ] was discovered in the 14th century by the Oxford Calculators of Merton College , and was proved ...
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.
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 linear motion can be of two types: uniform linear motion, with constant velocity (zero acceleration); and non-uniform linear motion, with variable velocity (non-zero acceleration). The motion of a particle (a point-like object) along a line can be described by its position x {\displaystyle x} , which varies with t {\displaystyle t} (time).
In physics, a dynamical system is described as a "particle or ensemble of particles whose state varies over time and thus obeys differential equations involving time derivatives". [3] In order to make a prediction about the system's future behavior, an analytical solution of such equations or their integration over time through computer ...
This is because when a particle on a streamline reaches a point, , further on that streamline the equations governing the flow will send it in a certain direction . As the equations that govern the flow remain the same when another particle reaches a 0 {\displaystyle a_{0}} it will also go in the direction x → {\displaystyle {\vec {x}}} .
Newton's cannonball is a thought experiment that interpolates between projectile motion and uniform circular motion. A cannonball that is lobbed weakly off the edge of a tall cliff will hit the ground in the same amount of time as if it were dropped from rest, because the force of gravity only affects the cannonball's momentum in the downward ...
Solving applications dealing with non-uniform circular motion involves force analysis. With a uniform circular motion, the only force acting upon an object traveling in a circle is the centripetal force. In a non-uniform circular motion, there are additional forces acting on the object due to a non-zero tangential acceleration.