**Kinetic Energy** The kinetic energy of a particle is given by:

where m is the particle's mass and v is the particles velocity.

**Work ** Work is energy transfered to or from an object by a force. Energy transtered to an object is posative work and energy transfered from an object is negative work. Work done by a constant force (F) over displacement (d) is given by:

Where the cosine of the angle between F and d is taken. If two forces act on one particle, the net work is equal to the work of each force combined, or the work done by the net force.

**Work and Kinetic Energy** Work is equal to the change in kinetic energy:

**Work done by Gravity** Work done by gravity is given by:

where m is the mass of the particle, g is 9.8, d is distance and the cosine of the angle between F_{g} and d is taken.

**Work Done Against Gravity** when lifting or lowering an object, the work done is euqal to:

If K_{i} and K_{f} are equal then this reduces to:

**Spring Force** The force applied by a spring is equal to:

where k is a constant, and d is the distance from the equilibrium point which the spring is stretched. Therefore, the spring force is a variable force.

**Work Done by a Spring Force** The work done by a spring on an object attached to the end of the spring is given by:

If x_{i} is equal to zero, then this reduces to:

**Work by a Variable Force** Work is the area under a Force vs. Position graph:

**Power** Power due to a force is the rate of change at which that force does work on an object. if the force does work during a time interval Δt then the average power over that time interval is:

For a force at an angle to the direction of travel (instantanious velocity v), the instantaneous power is equal to:

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All information and equations are taken from and credited to Jearl Walker's Fundamental Physics.