Kinematics

Kinematics describes how objects move, as opposed to dynamics, which describes why objects move (see Kinematics vs Dynamics).

Kinematic Variables

Here are some important kinematics variables:

• Position, usually using or . Sometimes you will see or as well.
• Velocity, usually using or . Velocity is the change in position over time. We can describe it using

or using calculus,

• Acceleration, usually using . Acceleration is the change in velocity over time. We can describe it using

or using calculus,

Kinematic Equations:

The main Kinematic Equations you will use when starting to learn physics are:

Note that these equations only apply for constant values

Derivation of Kinematic Equations

First Equation

Second Equation

Third Equation

Then plug it into our second equation.

From this we can get the equation:

Additionally,

Note once again that these equations only work for constant values! Otherwise it is best to use calculus to solve problems.

Problems:

Problem 1. A ball is launched on the axis from with velocity . There is an unknown force causing an acceleration on the ball of . Find:

1. the equation of the position of the ball over time
2. the position at 5 seconds.
3. The time such that .

Problem 2. The acceleration of an unknown object is given by the equation . Find the equation of the position of the ball given time .