#### Kinematic equations for one-dimensional motion with constant acceleration

a_{x} = (v_{xf} - v_{xi})/∆t, where ∆t =
(t_{f} - t_{i}).

v_{xf }= v_{xi }+ a_{x }∆t.

v_{x(avg) }= (v_{xf }+ v_{xi})/2.

x_{f }- x_{i }= v_{xi}∆t + ½ a_{x}∆t^{2}.

v_{xf}^{2 }= v_{xi}^{2 }+ 2a_{x}(x_{f
}- x_{i}).

#### Projectile motion

v_{x} = v_{0x}, ∆x = v_{0x}t, v_{y} = v_{0y}
- gt, y = y_{0} + v_{0y}t - ½ gt^{2}.

#### Hooke's law

F = -kx

#### Work, energy and power

W = **F·d** ,

The work done by a force can be positive or negative. If the component of
the force in the direction of the displacement is positive, the work is
positive, and if the component of the force in the direction of the displacement
is negative, the work is negative.

Kinetic energy: K = ½mv^{2}.

Gravitational potential energy: U_{g} = mgh (with ground as reference).

Elastic potential energy: U_{s} = ½ kx^{2}.

P = ∆W/∆t

#### Friction

f_{s}≤ μ_{s}N, f_{k} = μ_{k}N.

#### Uniform circular motion:

Centripetal acceleration: a_{c} = v^{2}/r.

Centripetal force: F_{c} = mv^{2}/r.