Topic
Date
Page #
Solving Kinematics Equations
Seed
Question
Before your quiz….describe the motion of each of the following objects using complete sentences.
#1
CLASS SET
#3
#2
#4
5-7 minutes
Exploration
(Individual
work.)
There are a variety of quantities associated with the motion of objects - displacement (and
distance), velocity (and speed), acceleration, and time. Knowledge of each of these quantities provides
descriptive information about an object's motion. The unknown parameters can be determined using
physics principles and mathematical equations (the kinematic equations). The kinematic equations are a
set of four equations that can be utilized to predict unknown information about an object's motion if
other information is known. The equations can be utilized for any motion that can be described as being
either a constant velocity motion (an acceleration of 0 m/s/s) or a constant acceleration motion. They
can never be used over any time period during which the acceleration is changing, you need calculus to
do that!
Each of the kinematic equations include four variables. If the values of three of the four variables are
known, then the value of the fourth variable can be calculated. In this manner, the kinematic equations
provide a useful means of predicting information about an object's motion if other information is known.
For example, if the acceleration value and the initial and final velocity values of a skidding car is known,
then the displacement of the car and the time can be predicted using the kinematic equations. This unit
will focus upon the use of the kinematic equations to predict the numerical values of unknown quantities
for an object's motion.
The five kinematic equations that describe an object's motion are:
Complete the following chart to identify variable and potential units (list at least 2 possible for each).
Term
Variable
Units
Term
Acceleration
Velocity
Change in
Position
Displacement
Final Velocity
Initial Velocity
Change in
Time
Final Position
Initial Position
Change in
Velocity
Variable
Units
The five kinematic equations that describe the mathematical relationship between the parameters that
describe an object's motion. In this part of the unit we will investigate the process of using the
equations to determine unknown information about an object's motion. This process involves the use of
GUESS method; a problem-solving strategy that will be used throughout this course. The strategy
involves the following steps:
a.
Identify and list the given information in variable form.
b.
Identify and list the unknown information in variable form.
c.
Identify and list the equation that will be used to determine unknown information from
known information.
d.
Substitute known values into the equation.
e.
Use appropriate algebraic steps to solve for the unknown information.
In addition to the GUESS method, you could draw a small diagram to have a visual of what is
happening in the problem and you should always check your answer to insure that it is reasonable
and mathematically correct.
The use of this problem-solving strategy in the solution of the following problem is modeled
in Examples A and B below.
1. Ima Hurryin is approaching a stoplight moving with a velocity of +30.0 m/s. The light turns yellow,
and Ima applies the brakes and skids to a stop. If Ima's acceleration is -8.00 m/s2, then determine
the displacement of the car during the skidding process. (Note that the direction of the velocity and
the acceleration vectors are denoted by a + and a - sign.)
Diagram:
+
Givens and Unknown:
vi=30.0 m/s
vf=0 m/s
a = -8.00 m/s/s
∆x=?
Determine Equation
based on the givens
and unknowns. Ask
yourself: “Which
equation has all of
these and nothing
more?”
Big Ideas
For Further
Contemplation
Equation:
Rearrange to
become:
Substitute with units, then Solve and
box your answer:
(0m/s)2-(30 m/s)2
2(-8.00 m/s/s)
56.25 m = ∆x
When Ima slammed on the brakes her
car skidded 56.25 meters before
stopping. Since Ima’s direction did not
change (and she was headed in a +
direction initially), the sign of her
displacement should be positive.
After these ideas have been discussed complete the practice problems using the
GUESS method in your PJ. Be organized and use on the space on pages 28-29. You
will have the rest of class today and tomorrow to practice this math and some more
graphing. You should check your answers with me as you go.
The Kinematics Equations
Questions or comments?