Basic Definitions

Position is indicated by the vector r. Displacement still represents distance traveled and specifies the direction.

If you start at position r_o and move to position r, your displacement Δr is

Δr = r - r_o

Velocity and acceleration are defined as they were in one dimension:
v =
dr

dt

a =
dv

dt

Constant acceleration equations

The 1-D equations are modified simply by adding an x or y subscript to all the vector variables. As in 1-D, the equations apply under the following conditions:

the acceleration is constant
the motion is measured from t = 0
plus and minus signs give directions for the vector components

The x-component equations

v_x = v_ox + a_x t

x - x_o = v_ox t + ½ a_x t²

x - x_o = ½ (v_ox + v_x) t

v_x ² = v_ox² + 2 a_x (x - x_o)

There is a similar set of equations for the y-direction. Simply replace all the x's by y's in the equations above.

IMPORTANT: When solving problems always keep the x-component data separate from the y-component data. The only thing that can be used in both sets of equations is time.

Projectile motion

Projectile motion is motion under the influence of gravity alone.

A thrown object is a typical example. Follow the motion from the time just after the object is released until just before it hits the ground.

Air resistance is neglected. The only acceleration is the acceleration due to gravity.