Understanding Motion
Linear Motion
Motion
• The motion of an object can only be recognized
when something is established as a basis of
comparison…a reference point
• We say an object is moving when its position
changes compared to that reference point
• For most day-to-day situations, the Earth, and
those things affixed to it, serve as a convenient
reference frame.
Position and Time
• These are the two most fundamental physical
quantities that can be measured to describe
an object’s motion.
• The relationship between these variables can
be discovered experimentally and modeled
using mathematics in both graphical and
equation form.
Position vs. Time Graphs
• The magnitude (size) of the slope tells us…
• The algebraic sign of the slope tells us…
• The magnitude and sign together tell us…
• The vertical intercept tells us…
• When this graph is a straight line we know…
The generic equation for a
linear graph is…
y = mx + b
In terms of the physical
quantities being plotted this
becomes…
x = mt + b
Position, x (m)
Position vs. Time Graphs
Time, t (s)
If we replace the slope and
intercept terms with what
they tell us we get…
x = vt + xi
Where v is the velocity (m/s)
and xi is the initial position
(m) of the object in motion
Position, x (m)
Position vs. Time Graphs
m=v
xi
Time, t (s)
x = vt + xi
• This equation (straight line with slope v and
intercept xi) is a model that describes the
relationship between position and time for an
object moving with constant velocity.
x = position of object after time, t
v = velocity of object (speed in a direction)
t = elapsed time
xi = starting position of the object
Constantly Accelerated Motion
(ball on a ramp)
• Position-time graphs are NOT linear, they are
quadratic… x  t2
– slope is NOT constant  Velocity is changing
• Velocity-time graphs are linear… v  t
– Slope is constant  The rate at which velocity is
changing is constant
SLOPE = ACCELERATION
v = at + vo
• This equation is a model describing the
relationship between velocity and time for an
object that is constantly accelerating
v – velocity after time, t
a – acceleration
t – elapsed time
vo – starting velocity
x=½
2
at
+ vot + xo
• This equation models the relationship
between position and time for constantly
accelerated motion
• This equation emerges from our ball on a
ramp data or it could be derived (we will!)
x = position after time, t
a = acceleration
vo = starting velocity
t = elapsed time
xo = starting position
Free Fall
• An object is considered to be in free fall when
it is only under the influence of gravity
• Objects in free fall near the surface of Earth
experience constant acceleration…
a = g = 9.80 m/s2 downwards
“Fall” is misleading
• An object can be in free
fall while it is traveling
upwards (only under
the influence of g)
– Slows down at a
constant rate equal to
the rate that a falling
object gains speed
Free Fall Equations
vavg = x/t
a = v/t
v = vo + at
x = vot + ½ at2
v2 = vo2 + 2a x
Often you will find x
changed to y when
working on vertical
motion problems
Nothing new here! Free fall
is constantly accelerated
motion so the kinematics
equations are all applicable.
Remember a = g = 9.80m/s2
(downward)
***When problem solving,
pay close attention to
direction of quantities!!!!
Sample Problem
• A volley ball is hit straight upward with a
speed of 6.0 m/s. If the volley ball starts 2.0 m
above the floor, how long will it be in the air
before hitting the floor?