Motion Graphs Describing the motion of an object is occasionally hard to do with words. Remember: 

 DistanceTime GraphsPlotting distance against time can tell you a lot about motion. Let's look at the axes: Time is always plotted on the Xaxis (bottom of the graph). Distance is plotted on the Yaxis (side of the graph). If an object is not moving, a horizontal line is shown on a distancetime graph. Time is increasing to the right, but the distance does not change. It is not moving. If an object is moving at a constant speed, it means it has the same increase in distance in
Time is increasing to the right, and distance is increasing constantly with time. Constant speed is shown by straight lines on a graph. Let’s look at three moving objects: All of the lines in the graph show that each object
A steeper line indicates a larger distance moved in a given time. All lines are straight, so both speeds are constant. Graphs that show acceleration look different from those that show constant speed. The line on this graph is curving upwards. This shows an increase in speed, In other words, in a given time, the distance the object moves is changing Graphs Summary: A distancetime graph tells us how far an object has moved with time.
A great online review game of motion graphing. Interpreting Graphs
Note: assume all examples, discussions and problems are

t 
d 
0.00 

0.05 

0.10 

0.15 

0.20 

... 
t 
d 
Δd 
v 
0.00 

0.05 

0.10 

0.15 

0.20 

... 
Astronaut dropping a feather and a hammer on the moon:
Average Velocity Teaser:
Suppose in making a round trip you travel at uniform speed of 30 mph from A to B
which are separated by 100 miles, and return from B to A at a uniform rate of 60 mph.
What would be your average speed for the round trip? (Careful!)
A car goes from 0 m/s to 160 m/s in 5 seconds
What is the acceleration?
a = (160m/s  0m/s)/5sec
a = 32m/s^{2}
Note on acceleration: It seems strange to have seconds "squared" since it is an
intangible quantity. If it helps, 32m/s^{2} can also be read as
32 meters per second per second, which means “for every second
the velocity changes by 32m/s”.
It is usually v = at but the vi is added in incase you are not starting from a rest.
“v is where it’s at”
v_{f} = v_{i} + at problem: (actually starting at rest so it is v_{f} = at)
What is the exit velocity of a bullet after it travels down a rifle barrel with
an acceleration of 2.0 x 10^{5} m/s^{2} in a time of .003 seconds?
v_{f} = v_{i} + at problem:
A rocket car is cruising down a road at 40 m/s using only the conventional
engine in the car. The driver then engages the rockets and the car accelerates
at a rate of 10 m/s^{2} until the engines cut off after 10 seconds of thrust.
What is the final velocity?
(Professional driver on a closed course. Do not attempt)
It is usually d = ½ at^{2} but you add in the v_{i}t in case you are already moving.
d = v_{i}t + ½at^{2} problem: (actually starting at rest so it is d = ½at^{2})
A model rocket provides an acceleration of 35 m/s^{2} for 6 seconds.
How high does the rocket reach when the engine cuts off?
d = v_{i}t + ½at^{2} problem:
A Klingon Bird of Prey is hurtling through space at 250 km/sec when it is
caught in the gravitational pull of the sun. At its current position, the
Bird of Prey’s acceleration due to the Sun’s gravity is 200 m/s^{2}.
The ship is subjected to this acceleration for 90 seconds before it slams into
the surface of the sun with an unimpressive “pop”. What was its final velocity?
Arsenal 4 worksheet: d = v_{i}t + ½at^{2} where v_{i} = 0
Arsenal 5 Worksheet: d = v_{i}t + ½at^{2}
Again, this equation is usually v_{f}^{2} = 2ad if you are starting from rest.
v_{f}^{2} = v_{i}^{2} +2ad problem: (actually starting at rest so it is v_{f}^{2} = 2ad)
A potato cannon accelerates a spud down a 1.2m tube at a rate of 1041m/s^{2}.
What is its final muzzle velocity?
Don’t forget the square root.
Arsenal 6 worksheet: v_{f}^{2} = v_{i}^{2} +2ad where v_{i} = 0
Arsenal 7 worksheet: v_{f}^{2} = v_{i}^{2} +2ad
Photo: Phil Medina, Jones Beach Memorial Day Air Show 2011
A10 Thunderbolt "Warthog" piloted by Major Thorpe.
An A10 Thunderbolt Warthog dives down for a strafing run on an enemy target
at a velocity of 89 m/s. It fires its cokebottlesized bullets down its 3 meter cannon
with an acceleration of 121,000 m/s^{2}. What is the bullet’s velocity when it slams into its target?
v = d/t
a = Δv/t
v_{f} = v_{i} + at
d = v_{i}t + ½at^{2}
v_{f}^{2} = v_{i}^{2} +2ad
Arsenal 8 worksheet: "Weapons of Math Destruction" Multiple equation problems
Each v means something different:
Free fall problems can often be solved by using:
v_{f} = v_{i} + at to find v or t
d = v_{i}t + ½at^{2 }to find d or t
or
v_{f}^{2} = v_{i}^{2} +2ad to find v or d
However, the v_{i} portion of the equation will turn into zero and can be crossed
out, if it drops from rest (v_{i} = 0). Mathematically, it will also work out the same
way (crossing out the v_{i} portion) if the object is thrown upwards and reaches the
peak (where its velocity will = 0)
You have been sent to Pluto by NASA to fix a 90meter high radio antenna.
The antenna must function in order for NASA to communicate with astronauts
sent to explore the planet Xena and its moon Gabrielle. While working on the
antenna, you drop your wrench. It takes the wrench 21.2 seconds to fall to the
cold surface of the Dwarf Planet. Calculate the acceleration due to gravity on Pluto.
If you jump up at 5.4 m/s, how long will you stay in the air (round trip)?
Could you jump back to the top of the antenna if you jump at 5.4 m/s?
Free Fall Problems 1
Free Fall Problems 2
Free Fall Problems 3
Establish which direction represents + or 
6 5 4 3 2 1 0 1 2 3 4 5 6
<>+
v+ a+ v a (same sign) 
= faster speed 
v+ a v+ a (opposite sign) 
= slower speed 