**UNIT 3 ****READING****
A**

**Two-Dimensional Motion**

The position of an object can be represented by a vector, as described in Unit 1 Reading B. The velocity of an object is then defined by:

_{}

where **x**_{f} is the final position vector, **x**_{i}
is the initial position vector, t_{f} is the final time, t_{i}
is the initial time. The velocity, **v**, is the rate of change of the
position vector. Because this is a vector equation, it is very hard to use in
this form and it is easier to understand, if it is separated into its x- and y-
components:

_{}

_{}

The acceleration is defined as

_{}

where **v**_{f} is the final velocity vector, **v**_{i}
is the initial velocity vector, t_{f} is the final time, t_{i}
is the initial time. The acceleration, **a**, is the rate of change of the
velocity vector. Because this is a vector equation, it is very hard to use in
this form and it is easier to understand, if it is separated into its x- and y-
components:

_{}

_{}

If the acceleration and the velocity are separated into their x- and y- components, then the equations of motion can be applied independently to the x- and y- directions:

_{} _{}