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:
v=
xf − xi
t f − ti
where xf is the final position vector, xi is the initial position vector, tf is the final time, ti 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:
vx =
xf − xi
t f − ti
vy =
y f − yi
t f − ti
a=
vf − vi
t f − ti
The acceleration is defined as
where vf is the final velocity vector, vi is the initial velocity vector, tf is the final time, ti 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:
ax =
ay =
vxf − vxi
t f − ti
vyf − vyi
t f − ti
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:
1
v xf + v xi
t
2
− v xi = a x t
yf - yi =
xf - xi =
v xf
v yf + v yi
2
v yf − v yi = a y t
1
x f - x i = v xi t + a x t 2
2
2a x (x f - x i ) = v 2xf − v 2xi
t
1
ayt2
2
2a y (y f - y i ) = v 2yf − v 2yi
y f - y i = v yi t +
2