Motion
(Chapter 2)
Student Learning Objectives
• Compare and contrast terms used to
describe motion
• Analyze circular and parabolic motion
How do speed and velocity compare?
Average speed is the
distance covered in some
amount of time.
Velocity is speed in some
direction.
Up, Down
Left, Right
N, S, E, W
–, +
s=d
t
Practice
An Olympic runner completes the 100
meter dash in 11 seconds.
a) What is the runner's average speed?
b) How fast is this in mph?
Scalar/Vector
 Scalars are quantities that indicate size, indicate a
numerical value.
 Vectors are quantities that indicate the size and direction.
 The magnitude of a vector is a scalar; it is the size of the
vector.
Example: 65 mph North
How is acceleration defined?
Acceleration is the
change of velocity in
some amount of time.
Deceleration is negative
acceleration. (opposite
direction of motion)
a = Dv
t
http://www.physicsclassroom.com/mmedia/kinema/pvpa.cfm
http://www.physicsclassroom.com/mmedia/kinema/pvna.cfm
http://www.physicsclassroom.com/mmedia/kinema/avd.cfm
A car that maintains a
constant speed in a
straight line has zero
acceleration.
The distance traveled
depends on how long
the object has been
accelerating.
d = (1/2)at2
Practice
1) When driving through a flat curve at a constant
rate of speed, is there acceleration? Explain.
More Practice
2) On the freeway, it takes 3 seconds to increase your
speed from 15 mph (6.7 m/s) to 65 mph (29 m/s).
a) What is the average acceleration?
b) If the car continues to accelerate, at the same rate, for
another 1.5 seconds, what will the final velocity be?
c) How far will the car have traveled during the 4.5
seconds of acceleration?
What causes vertical acceleration?
 Objects are accelerated downward because of gravity.
 The gravitational pull from the Earth is the same on
all objects, so the downward acceleration is the same
on all objects, 9.81 m/s2.
 Any difference in the net acceleration is due to air
resistance.
Practice
1) I toss a ball upward and it returns to my hand.
What is the ball’s rate of acceleration if there is
no air resistance?
a) Just after the ball leaves my hand?
b) At the top of the trajectory?
c) Just before the ball hits the ground?
More Practice
2) Professional cliff divers fall from a cliff into
the sea.
a) If the dive takes 2.7 seconds, what is the distance
they fall?
b) What would be the speed of the diver as the diver
enters the water?
What is terminal velocity?
 An object in free fall is only affected by gravity (no air
resistance).
 Air resistance provides acceleration upward.
Surface Area
Speed
 Terminal velocity occurs when air resistance balances
gravity.
http://www.physicsclassroom.com/mmedia/newtlaws/sd.cfm
What causes circular motion?
 Objects move in a straight
line, unless an unbalanced
force changes the motion.
 In circular motion, a
centripetal force
(“center-seeking” force)
causes a constant change
in motion, a constant
change in direction.
ac = v2
r
Fc = mac
http://www.physicsclassroom.com/mmedia/circmot/ucm.cfm
Practice
1) Describe some examples of centripetal
motion.
More Practice
2) An object is circling two times every second at the
end of an 8 cm long string.
a) Determine how to calculate the velocity, and calculate
it. (Hint: what is the distance?)
b) Calculate the centripetal acceleration.
c) Calculate the amount of centripetal force on a 0.5 kg
object.
Why does a projectile have a parabolic trajectory?
 The addition of the horizontal velocity and the vertical
acceleration due to gravity results in a curved path.
A projectile's motion in x does not affect its motion
in y! (and vice versa)
Velocity in x is constant if there is no air resistance.
Why?
Velocity in y changes. Why?
http://www.physicsclassroom.com/mmedia/vectors/hlp.cfm
http://www.physicsclassroom.com/mmedia/vectors/pap.cfm
 A projectile will fall a
vertical distance (y) each
second after reaching
maximum height.
y = (1/2)gt2
 The range (x) of a
projectile relative to the
horizontal plane depends
on the object’s horizontal
velocity and time of
flight.
x = vt
Practice
1) At what angle relative to the ground should a football
be thrown to have the greatest horizontal range?
2) What are some examples of projectile motion that
you have observed?
More Practice
3) A player throws a baseball parallel to the ground with a
horizontal velocity of 90 mph (40 m/s). Assume no air
resistance.
a) What is the direction of the acceleration?
b) Does the horizontal speed change? Does the vertical
speed change?
c) What is the horizontal speed the instant before the ball hits
the ground?
d) If there was no gravity, what would be the path of the ball?
Why?
The Range
e) What is the maximum horizontal range of the
baseball if it is released from a height of 1.5
meters at 40 m/s?