Motion Notes
Motion happens when an object changes its position. Reference
points are used to determine if something is moving or not.
A reference point is a place or object used for comparison to
determine if an object is in motion. If there is a change in distance
between the reference point and the object, then the object is in
motion.
Using the man in the car as our
reference point, the dog is not
moving.
Using the white car as our
reference point, the dog is
moving.
How do you know the mail truck has moved?
(What did you use as a reference point? ______________________)
Distance – is how far something has moved. In order to
find out what sort of motion takes place, distance needs
to be measured. The SI unit of length or distance is
meters (m).
Displacement/Position – is the distance and direction of
an object’s change in position from the starting point.
In the picture on the right, label letters A and B as being either
displacement or distance.
A = __________________________
B = __________________________
How far has this runner
been displaced from
the starting line?
(What’s the position from
the starting line?)
___________________
What is the total
distance this runner
has ran?
___________________
Speed – is how far something travels in a given amount of
time or the distance traveled per amount of time.
• The variable for speed is S
• The SI unit for speed is m/s (meters per second)
Example: A cyclist traveled 100 miles in 10 hours. What
was his speed?
Variables: d =
Formula:
Solve:
t=
S=
Much of the time, the speeds you experience are not constant. Think
about riding a bicycle for a distance of 5 km. As you start out, your
speed increases from 0 km/h to, say, 20 km/h.
You slow down to 10 km/h
as you pedal up a steep hill
and speed up to 30 km/h
going down the other side
of the hill. You stop for a red
light, speed up again, and
move at a constant speed
for a while. As you near the
end of the trip, you would
slow down and then stop.
Checking your watch, you find that the trip took 15 min, or one-quarter
of an hour. How would you express your speed on such a trip? Would
you use your fastest speed, your slowest speed, or some speed
between the two?
Average speed – is the total distance traveled over the
total amount of time.
Formula: Average speed = Total distance/Total time
or
Savg = dtotal/ttotal
Example: A person walks 4 miles in 2 hours then stops for
an hour for lunch. After lunch they walk 8 miles in 3
hours. Calculate the person’s average speed.
Variables:
Formula:
Solve:
DISTANCE
4 miles
0 miles
8 miles
12 total mi
TIME
2 hours
1 hour
3 hours
6 total hrs
CAREFUL!
Distance is 0 miles because
“stopped for lunch”.
Instantaneous Speed
Suppose you watch a car’s speedometer go from 0 km/h to 60
km/h. A speedometer shows how fast a car is going at one point in
time or at one instant. The speed shown on a speedometer is the
instantaneous speed.
Instantaneous speed – is the speed at a given point in time.
Graphing Motion as CONSTANT SPEED
Graphing Conventions: The dependent variable is always on the y-axis.
DRY
The independent variable is always on the x-axis.
MIX
Examples of units of Speed: km/s, km/h, m/s, mi/h, cm/yr …
Faster constant speed
Slower constant speed
Start, stop, start
Time is always an independent
variable (x-axis).
Graph 1
Distance or Position
vs. Time Graph
Slope = speed
(Slope is rise/run)
(Speed is distance/time)
The slope (or speed) of
a flat line is zero or no
speed. The object is at
rest (stopped).
Graph 2: A car travels at a constant speed of 6 m/s
(S = 30 m/5 s). The graph of constant speed is a slanted straight
line. Notice that the speed is the same at every point on the graph.
How far does the car go in 4 seconds?
Variables:
Formula:
Solution:
S = 6 m/s;
t = 4 s; d = ?
Graph 3: The same car travels at a constant speed of 1.0 m/s (S = 10 m/10 s).
The graph of constant speed is a slanted straight line. Notice that the slope of
the line is more gradual and every point on the graph has the same speed.
How far does the car go in 4 seconds at its new speed?
Variables:
Formula:
Solution:
S = 1.0 m/s;
t = 4 s; d = ?
Velocity
Escalators are found in
shopping malls and airports.
The up and down escalators
move their passengers at a
constant speed, but in
opposite directions. The
speeds of the passengers are
the same, but their velocities
are different because the
passengers are moving in
different directions.
Velocity – includes the speed of an object and the direction of its
motion.
VELOCITY = Distance/time AND direction
Example: 5,000 m/s south
*** Velocity is calculated like speed
but a direction is given.
The speed of this car is constant,
but its velocity is not constant
because the direction of motion is
always changing.
Example: A car moving northward at 60 km/hr passes a car moving
southward at 60 km/hr. Both have the same speed but each has a
different velocity.
Acceleration
Acceleration – is the rate of change of velocity. This includes changes
in speed, direction, or both. If an object changes velocity, it is
accelerating. An object that slows, speeds up, turns, or stops, is
accelerating.
PRACTICE PROBLEMS:
1.What would be the velocity of a storm moving west, if it
traveled at 108 km in 2 hours?
2.What is your average velocity if you travel east for a
distance of 300 miles in 2.5 hours?
3.A storm is moving east at a velocity of 60 km/hr. If the
storm is 140 km west of our location, how many hours
will it take for the storm to reach us?
1.
2.
3.
4.
5.
WHICH OF THE FOLLOWING SHOWS A CHANGE IN
ACCELERATION???
The red Mustang maintains its speed between points A and B.
Between points B and C the Mustang increases speed on the long
stretch.
Between C and D the car changes direction heading south and
slows in speed.
There was a roadside park at D so the driver stopped and rested.
There were store windows between D and E and the driver slowed
the car’s speed to a creep.
Acceleration
Example: A plane starts at rest and ends up going 200 m/s in 10 seconds.
Calculate the acceleration.
Step 1: Variables: Vi = starting speed = 0 m/s (“starts at rest”);
Vf = ending speed = 200 m/s, ∆t =10s
Deceleration (Negative Acceleration)
Example: A race car starts at 400 m/s and then stops in 20 seconds. Calculate the
car’s acceleration.
Step 1: Variables: Vi =400 m/s; Vf = 0 m/s; ∆t = 20 m/s
*** Take note of the negative sign.
This represents deceleration or
slowing down.
Gravity
Acceleration due to gravity is always a constant 9.8 m/s2.
PRACTICE PROBLEMS
1. A biker starts to move and goes from 0 m/s to 25 m/s
in 10 s. What is the acceleration?
Variables:
2. A biker goes from a speed of 20 m/s to 8 m/s in 6 s.
What is the acceleration?
Variables:
3. A driver starts his parked car and attains an acceleration
of 3 m/s2 in 5 seconds. What is the final speed?
Variables:
A slow-moving object is easier to
stop than a fast-moving object.
Increasing either the speed or
mass of an object makes it
harder to stop.
A moving object has a property called momentum that is
related to how much force is needed to change its motion.
The momentum of an object is the product of its mass and
velocity. Momentum is given the symbol p and can be
calculated with this equation:
p=mxv
Momentum = mass x velocity
The unit for momentum is kg m/s. Note that momentum
has a direction because velocity as a direction.
In the picture at right, the two trucks
might have the same velocity, but the
bigger truck has more momentum
because of its greater mass.
An archer’s arrow can have a large
momentum because of its high velocity,
even though its mass is small. A walking
elephant may have a low velocity, but
because of its large mass, it has a large
momentum.
Law of Conservation of Momentum
The momentum of an object doesn’t change unless its
mass, velocity, or both change. Momentum, however,
can be transferred from one object to another.
Momentum is transferred in collisions. Consider a game of pool.
Before the game starts, all the balls are motionless. The total
momentum of the balls is, therefore, zero. What happens when the
cue ball hits the group of balls that are motionless? The cue ball slows
down and the rest of the balls begin to move. The total momentum
of all the balls just before and after the collision would be the same.
The momentum the group of balls gained is equal to the momentum
that the cue ball lost. The total momentum is conserved—it isn’t
created or lost.
The results of a collision depend on the momentum of each
object. When a puck hits another puck from behind, its
gives the second puck momentum in the same direction. If
the pucks are speeding toward each other with the same
speed, the total momentum is zero. (How will they move
after they collide?)