Kinematics – Defining Motion
http://www.aplusphysics.com/courses/honors/kinematics/honors_kinematics.html
Unit #2 Kinematics

Objectives and Learning Targets
 Understand the difference between distance and
displacement and between speed and velocity.
 Calculate distance, displacement, speed, velocity,
and acceleration.
 Solve problems involving average speed and
average velocity.
Unit #2 Kinematics
Defining Motion
 Position - refers to an objects location at any given
point in time. Position is a vector, and its magnitude
is given by the symbol x.
 Distance – is how far an object travels (in one
dimension at a type) from its initial position.
Distance is a scalar. It has a magnitude, or size, only.
The basic unit of distance is the meter (m).
Unit #2 Kinematics
Sample Problem #1
 On a sunny afternoon, a deer walks 1300
meters east to a creek for a drink. The deer
then walks 500 meters west to the berry
patch for dinner, before running 300 meters
west when startled by a loud raccoon. What
distance did the deer travel?
Unit #2 Kinematics
Sample Problem #1
 On a sunny afternoon, a deer walks 1300
meters east to a creek for a drink. The deer
then walks 500 meters west to the berry patch
for dinner, before running 300 meters west
when startled by a loud raccoon. What
distance did the deer travel?

Answer: The deer traveled 1300m +
500m + 300m, for a total distance
traveled of 2100m.
Unit #2 Kinematics
Displacement
 Different from distance, displacement – is how far
an object is from its starting point, or its change in
position.
Unit #2 Kinematics

The vector quantity displacement Δx = (x-x0)
describes how far an object is from its starting
point, and the direction of the displacement vector
points from the starting point to the finishing point.

Like distance, the units of displacement are meters
(m).
Sample Problem #2
 A deer walks 1300 m east to a creek
for a drink. The deer then walked
500 m west to the berry patch for
dinner, before running 300 m west
when startled by a loud
raccoon. What is the deer’s
displacement?
Unit #2 Kinematics
Sample Problem #2
 A deer walks 1300 m east to a creek
for a drink. The deer then walked
500 m west to the berry patch for
dinner, before running 300 m west
when startled by a loud
raccoon. What is the deer’s
displacement?
 Answer: The deer’s displacement
was 500m east.
Unit #2 Kinematics
Sample Problem #3
Unit #2 Kinematics

Sample Problem #3
Unit #2 Kinematics

Speed and Velocity

Knowing only an object's distance and displacement doesn't tell the whole
story. Going back to the deer example, there's a significant difference in the
picture of the deer's afternoon if the deer's travels occurred over 5 minutes 300
seconds) as opposed to over 50 minutes (3000 seconds).

How exactly does the picture change? In order to answer that question, you'll
need to understand some new concepts – average speed and average velocity.

Average speed, given the symbol , is defined as distance traveled divided by
time, and it tells you the rate at which an object's distance traveled changes.
When applying the formula, you must make sure that x is used to represent
distance traveled.
Unit #2 Kinematics
Sample Problem #4
 A deer walks 1300 m east to a creek for a
drink. The deer then walked 500 m west to
the berry patch for dinner, before running
300 m west when startled by a loud
raccoon. What is the deer's average speed
if the entire trip took 600 seconds (10
minutes)?
Unit #2 Kinematics
Sample Problem #4
 A deer walks 1300 m east to a creek for a
drink. The deer then walked 500 m west to
the berry patch for dinner, before running
300 m west when startled by a loud
raccoon. What is the deer's average speed
if the entire trip took 600 seconds (10
minutes)?
 Answer:
Unit #2 Kinematics
Average Velocity
 Average velocity, also given the symbol
, is defined
as displacement, or change in position, over time. It
tells you the rate at which an object's displacement,
or position, changes. To calculate the average
velocity, you divide the displacement by time
(remember it’s a vector)
Unit #2 Kinematics
Sample Problem #6
 A deer walks 1300 m east to a creek for a drink. The deer then
walked 500 m west to the berry patch for dinner, before running
300 m west when startled by a loud raccoon. What is the deer's
average velocity if the entire trip took 600 seconds (10
minutes)?
Unit #2 Kinematics
Sample Problem #6
 A deer walks 1300 m east to a creek for a drink. The deer then
walked 500 m west to the berry patch for dinner, before running
300 m west when startled by a loud raccoon. What is the deer's
average velocity if the entire trip took 600 seconds (10
minutes)?
 Answer:
Unit #2 Kinematics
Avg. Speed vs. Avg. Velocity
 Notice how the answers for each are vastly
different, the main reason is because distance and
speed are scalars; while displacement and velocity
are vectors.
 A good way to memorize is …
 Speed = Scalar
 Velocity = Vector
Unit #2 Kinematics
Sample Problem #7
 Chuck the hungry squirrel travels 4m east
and 3m north in search of an acorn. The
entire trip takes him 20 seconds. Find:
Chuck’s distance traveled, Chuck’s
displacement, Chuck’s average speed,
and Chuck’s average velocity.
Unit #2 Kinematics
Sample Problem #7
 Chuck the hungry squirrel travels 4m east
and 3m north in search of an acorn. The
entire trip takes him 20 seconds. Find:
Chuck’s distance traveled, Chuck’s
displacement, Chuck’s average speed, and
Chuck’s average velocity.
 Answer:
Unit #2 Kinematics
Acceleration
 What would happen if velocity never changed?
 Objects would move at the same speed and direction having
the same kinetic energy and momentum.
 Acceleration – the rate at which the velocity of an object
changes
Unit #2 Kinematics
Acceleration

This indicates that the change in velocity divided by the time interval
gives you the acceleration

Acceleration is a vector – it has a direction

the units of acceleration are meters per second per second, or [m/s2]

the units mean is that velocity changes at the rate of one meter per
second, every second

an object starting at rest and accelerating at 2 m/s2 would be moving at 2
m/s after one second, 4 m/s after two seconds, 6 m/s after 3 seconds,
and so on

Special note is the symbolism for v. The delta symbol ( ) indicates a
change in a quantity, which is always the initial quantity subtracted from
the final quantity. For example:
Unit #2 Kinematics
Sample Problem #8
 Monty the Monkey accelerates uniformly
from rest to a velocity of 9 m/s in a time
span of 3 seconds. Calculate Monty's
acceleration.
Unit #2 Kinematics
Sample Problem #8
 Monty the Monkey accelerates uniformly
from rest to a velocity of 9 m/s in a time
span of 3 seconds. Calculate Monty's
acceleration.
 Answer:
Unit #2 Kinematics
Rearranging Acceleration
 The definition of acceleration can be rearranged to
provide a relationship between velocity,
acceleration and time as follows:
Unit #2 Kinematics
Sample Problem #9
 The instant before a batter hits a 0.14-
kilogram baseball, the velocity of the ball is 45
meters per second west. The instant after the
batter hits the ball, the ball's velocity is 35
meters per second east. The bat and ball are
in contact for 1.0×10-2 second. Determine the
magnitude and direction of the average
acceleration of the baseball while it is in
contact with the bat.
Unit #2 Kinematics
Sample Problem #9
 Answer:
Unit #2 Kinematics
+ and - Accelerations
 Because acceleration is a vector and has direction, it's important
to realize that positive and negative values for acceleration
indicate direction only.
 Take a look at some examples…
 http://www.aplusphysics.com/courses/honors/kinematics/hono
rs_motion.html
 Be careful with + and – vectors. A + accelerations does not
always mean moving to the right, or a – mean moving left
 See Phet examples
Unit #2 Kinematics