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From the equation for uniform linear acceleration, the distance covered = + for initial speed =, constant acceleration (acceleration due to gravity without air resistance), and time elapsed , it follows that the distance is proportional to (in symbols, ), thus the distance from the starting point are consecutive squares for integer values of time elapsed.
The speed attained during free fall is proportional to the elapsed time, and the distance traveled is proportional to the square of the elapsed time. [39] Importantly, the acceleration is the same for all bodies, independently of their mass.
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.
The average speed of an object in an interval of time is the distance travelled by the object divided by the duration of the interval; [2] the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero. Speed is the magnitude of velocity (a vector), which indicates additionally the direction of ...
The general formula for the escape velocity of an object at a distance r from the center of a planet with mass M is [12] = =, where G is the gravitational constant and g is the gravitational acceleration. The escape velocity from Earth's surface is about 11 200 m/s, and is irrespective of the direction of the object.
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 = = =.
Pace is the reciprocal of speed. It can be calculated here from the following formula: [6] [19] p = p0·(1 + α·m) where: p = pace p0 = pace on flat terrain m = gradient uphill. This formula is true for m≥0 (uphill or flat terrain). [6] [19] It assumes equivalence of distance and climb by applying mentioned earlier α factor. [4] [19]
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.)