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: