2-Dimensional Motion

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The motion of an object can occur in one dimension, two dimensions and three dimensions. One dimensional motion occurs along one axis such as x. Two dimensional motion occurs when an object moves along two axes, such as x and y. Three dimensional motion occurs in the three axes of motion: x, y and z, which provides the most accurate representation of the reality.

The Main Idea

Two Dimensional Motion is a model to extrapolate the properties of an object moving along two axes, usually x axis and y axis. The properties of an object include it's position, velocity and acceleration. Two dimensional motion has two vector components derived from each axis of motion.

A Mathematical Model

[math]\displaystyle{ \begin{align} v & = at+v_0 \quad [1]\\ \end{align} }[/math]

[math]\displaystyle{ \begin{align} d & = d_0 + v_0 t + \frac{{a}t^2}{2} \quad [2]\\ \end{align} }[/math]

[math]\displaystyle{ \begin{align} d & = d_0 + \left( \frac{v+v_0}{2} \right )t \quad [3]\\ v^2 & = v_0^2 + 2a\left( d - d_0 \right) \quad [4]\\ d & = d_0 + vt - \frac{{a}t^2}{2} \quad [5]\\ \end{align} }[/math]

Examples

Simple

Dr.Greco stands on a 50ft high cliff in his penguin suit and throws a ball his friend who is standing 50 ft away from the cliff. What is the y component of velocity if it takes 10 seconds for the ball to reach his friend?

d & = d_0 + \left( \frac{v+v_0}{2} \right )t \quad [3]\\

History

Motion of an objects has been studied since the time of Aristotle. However, it was not until Galileo's experimentation with inclined planes did we really discover the concept of 2 D motion.1

See also

• Speed and Velocity
• Acceleration
• 3-Dimensional Position and Motion

Further reading

http://www.physicsclassroom.com/class/vectors http://physics.bu.edu/~duffy/py105/Motion2D.html

External links

https://www.khanacademy.org/science/physics/two-dimensional-motion

References

1.http://galileo.rice.edu/lib/student_work/experiment95/paraintr.html 2.https://en.wikipedia.org/wiki/Equations_of_motion