Unit 2.3 Problem Solving
Teacher: Dr. Van Der Sluys
Objectives
• The Kinematic Equations
• Word Problems
– Reading the question
• Identifying the goal of the question
• Identifying the variables
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–
–
–
–
Identifying the correct equation
Inserting the variables into the equation
Doing the algebra/math
The importance of including units
Reporting the answer
The Four Kinematic Equations
x = x0 + v0t + 12at2
v = v0 + at
v2 = v02 + 2ad
v=
v + v0
2
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x = x0 + v0t + 2 at2
•
•
•
•
•
x = final position
x0 = initial position or position at zero time
v0 = initial velocity at zero time, usually in m/s or km/hr
t = the amount of time elapsed, usually in seconds.
a = acceleration in m/s2
d = v0t + 12 at2
•
d = x - x0
distance, in meters, traveled in the given amount
of time.
v = v0 + at
Symbol
Definition
Unit
v
v0
a
t
v2 = v02 + 2ad
Symbol
Definition
Unit
v
v0
a
d
2
v = v + v0
2
Symbol
Definition
Unit
v
v
v0
Word problems (pg 29)
• Reading the question
– Identifying the goal of the question
– Identifying the variables
•
•
•
•
•
Identifying the correct equation
Inserting the variables into the equation
Doing the algebra/math
The importance of including units
Reporting the answer (and does it make
sense? If not go back and trouble shoot.)
Example Word Problem
How long does it take a car to cross a 25.0 m
wide intersection after the light turns green, if it
accelerates from rest at a constant 2.00 m/s2 ?
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Example Word Problem
How long does it take a car to cross a 25.0 m
wide intersection after the light turns green, if it
accelerates from rest at a constant 2.00 m/s2 ?
What is the goal of the question?
Time or t
Example Word Problem
How long does it take a car to cross a 25.0 m
wide intersection after the light turns green, if it
accelerates from rest at a constant 2.00 m/s2 ?
What variables are given?
d = 25.0 m
a = 2.0 m/s2
v0 = ?
Example Word Problem
How long does it take a car to cross a 25.0 m
wide intersection after the light turns green, if it
accelerates from rest at a constant 2.00 m/s2 ?
What equation do we use? List the variables
given in the problem and the goal. Look for an
equation that has these variables.
t = ? d = 25.0 m a = 2.0 m/s2 v0 = 0
d = v0 t +
1/2
at2
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Example Word Problem
How long does it take a car to cross a 25.0 m
wide intersection after the light turns green, if it
accelerates from rest at a constant 2.00 m/s2 ?
Insert all of the variables given into the
equation.
25.0 m = (0)t + 1/2 (2.0 m/s2)t2
Example Word Problem
How long does it take a car to cross a 25.0 m
wide intersection after the light turns green, if it
accelerates from rest at a constant 2.00 m/s2 ?
Simplify and rearrange the equation using the
basic rules of algebra to isolate the variable
that is the goal.
25.0 m = 1/2 (2.0 m/s2)t2
Example Word Problem
How long does it take a car to cross a 25.0 m
wide intersection after the light turns green, if it
accelerates from rest at a constant 2.00 m/s2 ?
Do the math (using a calculator if necessary).
Check to make sure the units cancel and give
the appropriate unit for the answer.
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Example Word Problem
How long does it take a car to cross a 25.0 m
wide intersection after the light turns green, if it
accelerates from rest at a constant 2.00 m/s2 ?
Does the answer make sense? If not go back
and trouble shoot to find where you may have
made an error.
Follow the Pattern Every Time
• If you follow this pattern you will never get
kinematic problems wrong.
• Be disciplined and don’t be lazy.
• Don’t take short cuts until you clearly have
become an expert.
• Don’t look at the answers in the back of the
book before doing the problem.
• Do be proud when you have struggled a little
and then finally get the answer. Good things
come to those who are stubborn.
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