Kinematics

Kinematics is the branch of classical mechanics that deals with pure motion of points, bodies (objects) and systems of bodies (groups of objects) without consideration of the causes of motion.  Kinematics is aptly referred to as the "geometry of motion."

To describe motion, kinematics studies the trajectories of points, lines and other geometric objects and their differential properties such as velocity and acceleration. In addition, Kinematics is used in astrophysics to describe the motion of celestial bodies and systems, and in mechanical engineering, robotics and biomechanics to describe the motion of systems composed of joined parts (multi-link systems) such as an engine, a robotic arm or the skeleton of the human body.

vCalc's Kinematics folder contains equations to compute the motion of objects and systems of objects.

Kinematics Equations

• -h=1/2(-g)Deltat^2
• Deltat = sqrt((2h)/g)
• Deltax = x_0 + v_0 t + 1/2 a t^2
• Deltay = 1/2 a_y Deltat^2
• R = ((2v^2)/g) sin(theta) cos(theta)
• theta = tan^(-1)((Deltay)/(Deltax))
• v = (Delta r)/(Delta t)
• v_x = (Deltax)/(Deltat)
• v_x = w*sqrt(g/(2h))
• v_x = w/(Deltat)
• v_x = w/sqrt((2h)/g)
• v_x= v cos(theta)
• v_y = v sin(theta)
• x = v_x*t
• y = 1/2 a_y(x/v_x)^2
• |FA| = mgsin(theta)
• |FA|=|FW|sintheta
• Acceleration (V2-V1/delta t)
• Acceleration - Two Observation Mean
• Acceleration [Deltav, Deltat]
• Average Circular Velocity
• Average Speed
• Ballistic Initial Vertical Velocity Component
• Ballistic Projectile Displacement - x(v_0,t,theta)
• Ballistic Projectile Displacement - y(t,theta, v_0)
• Ballistic Range (Earth gravity)
• Ballistic Velocity to Achieve Height
• Ballistic X Position
• Ballistic X Velocity
• Ballistic Y Position
• Ballistic Y Velocity
• Change in Mass
• Change in Velocity
• Constant Acceleration
• delta t = f(arc,v)
• Delta t = theta* r / |v|
• Delta V
• Distance (Velocity, Time)
• Distance - constant acceleration
• Distance - constant velocity
• Distance - initial velocity and constant acceleration
• Distance Traveled
• Distance-Time-Velocity
• Duration of Force to Achieve Velocity
• Escape Velocity
• Final Velocity - f(a,dx)
• Free Fall (distance)
• Free Fall (time)
• Horizontal Velocity Component (ballistic)
• Initial Velocity
• Kinetic Energy
• Kinetic Energy [m,v]
• lever (downward force)
• Magnitude of Acceleration
• Magnitude of Position
• Magnitude of Velocity
• Mean Velocity
• Power [Force,Distance,Time]
• Projectile Motion - Vertical Displacement
• Restoring Torque on Physical Pendulum
• Sum of Masses
• Time [Distance, Velocity]
• Time from Distance and Acceleration
• Time of Motion
• Total Torque
• VBLx
• Velocity (constant ac