Kinematics

Kinematics is a field of classical mechanics that describes motion of particles and bodies without considering the forces that cause them to move.

Relevant pages

• Kinematic equations
• Projectile motion

The basics

Kinematics relies heavily on vector analysis. Distance and speed are scalar quantities, but their counterparts displacement and velocity are vector quantities. Distance is the magnitude of the displacement, and speed is the magnitude of the velocity. Both vector quantities have a direction and magnitude.

We typically first relate displacement, velocity, and acceleration in high school in terms of changes with respect to time.

$$a=\frac{\Delta v}{\Delta t};v=\frac{\Delta s}{\Delta t}$$

These actually describe the average velocity and average acceleration. We formally instead relate the three with differentiation and integration.

$$a=\frac{dv}{dt}=\frac{d^{2}s}{d{t}^2}$$ $$v=\int adt=\frac{ds}{dt}$$ $$s=\int vdt$$