Kinematics
• Kinematics is the branch of mechanics that describes
the motion of objects without necessarily discussing
what causes the motion.
• We will learn to describe motion in three ways.
– Using words
– Using graphs
– Using equations
Particle
• A particle is an object that has mass but no
volume and occupies a position described by
one point in space.
• Physicists love to turn all objects into particles,
because it makes the math a lot easier.
Position
• How do we represent a point in space?
a) One dimension
b) Two dimensions
c) Three dimensions
As an object moves, its position
undergoes change
Two quantities describe changing position
Distance
VS
Displacement
displacement
The length of the path
The length and direction
traveled
of a straight line path
from the beginning to the
distance
end position
Sometimes the path traveled is a straight line
distance = displacement
Displacement will never be greater than distance
Distance (d)
• The total length of the path traveled by a
particle is called distance.
• “How far have you walked?” is a typical
distance question.
• The SI unit of distance is the meter.
Displacement
• The change in the position of a particle in a
certain direction
• Δ is a Greek letter used to represent “change in “.
Δx therefore means “change in x”. It is always
calculated by the final value minus the initial
value
• “How far are you from home” is a typical
displacement question
• The SI unit for displacement is the meter
• Calculation of displacement
x  x f  xi
Distance vs Displacement
B
100 m
displacement
50 m
A
distance
• A picture can help you distinguish between distance
and displacement.
STOP
Vectors and scalars
Quantities that have both size, also called magnitude, and direction, are
called vectors. Displacement is a change in position in a certain direction.
It is a vector quantity.
Quantities that are just magnitude, numbers without any direction, such as
distance, time, or temperature, are called scalars.
In one dimensional motion,
the displacement direction is often given
as positive(+) or negative( )
A displacement of +3.5 m implies movement of
3.5 m in the positive direction.
A displacement of 3.5 m implies movement of
3.5 m in the negative direction.
Positive and negative directions are
chosen arbitrarily, but usually agree with
standard mathematical conventions.
Question
True or False: An object can be moving for 10
seconds and still have zero displacement.
a. True
b. false
If the above statement is true, then describe an
example of such a motion.
If the above statement is false, then explain why
it is false.
Question
A cross-country skier moves from location A to location B to location C to
location D. Each leg of the back-and-forth motion takes 1 minute to complete;
the total time is 3 minutes.
a. What is the distance traveled by the skier during the three minutes of
recreation?
b. What is the net displacement of the skier during the three minutes of
recreation?
Example
You are driving a car on a circular track of diameter 40 meters. After you
have driven around 2 ½ times, how far have you driven, and what is your
displacement?
The average velocity of an object is defined as
the ratio of its change in position to the
time taken to change the position.
It is the rate at
which
displacement
occurs
x
v= t
Velocity
is a vector
quantity
v = average velocity; in units of m/s
x = change in position, or displacement;
in units of m
t = change in time; in units of s
The “sign” of the velocity indicates
the direction of movement.
A positive sign indicates movement
in the positive direction.
A negative sign indicates movement
in the negative direction.
Speed is the magnitude of velocity.
It is a scalar and has no direction given with it.
Average speed is the total distance traveled
divided by the total time taken.
Average velocity is the total displacement
divided by the total time taken.
Average speed and average velocity are not always equivalent because
total distance and total displacement are not always the same.
Speed is the absolute value of velocity.
It is always a positive value.
Example
How long will it take the sound of the starting gun to reach the ears of
the sprinters if the starter is stationed at the finish line for a 100 m race?
Assume that sound has a speed of about 340 m/s.
Example
You drive in a straight line at 10 m/s for 1.0 km, and then you drive in a
straight line at 20 m/s for another 1.0 km. What is your average velocity?
Acceleration (a)
• Any change in velocity over a period of time is
called acceleration.
• The sign (+ or -) of acceleration indicates its
direction.
• Acceleration is occurring when an object…
– speeds up
– slows down
– Turns (changes direction)
Questions
• If acceleration is zero, what does this mean
about the motion of an object?
• Is it possible for a racecar circling a track to
have zero acceleration?
Average Acceleration.
In AP Physics B we only consider situations
where acceleration is constant.
This allows us to use the following formula
v f - vi
a= t
a = average acceleration;
in units of m/s2
vf = final velocity; in units of m/s
vi = initial velocity; in units of m/s
vf – vi = change in velocity
t = time for the change to occur; in units of s
Acceleration in 1-D Motion
has a sign!
• If the sign of the velocity and the sign of the
acceleration is the same, the object speeds
up.
• If the sign of the velocity and the sign of the
acceleration are different, the object slows
down.
Kinetics Equations
v=
x
t
useful but not on the AP formula sheet
v=
a=
𝑣𝑓 −𝑣𝑖
𝑡
vf2 = vi2 + 2ax
x = vit +
1 2
at
2
𝑉𝑓+𝑣𝑖
2
Example
You are designing an airport for small planes. One kind of airplane that might use this
airfield must reach a speed before takeoff of at least 28 m/s, and can accelerate at 2.00
m/s2. What must the minimum length of the runway be?
Example
A car traveling at 90 km/h strikes a tree. The front end of the car compresses and the
driver comes to a rest after traveling 0.80 m. How long did it take the car to come to a
stop?