Physics 30S
What is Kinematics?
• Kinematics describes the motion of objects.
• How do things move?
• What is displacement, velocity and
acceleration?
Outcomes
• S4P-1-1 Derive the special equations for constant
acceleration. Include:
• S4P-1-2 Solve problems for objects moving in a
straight line with a constant acceleration.
Include:
• S4P-1-3 Solve relative motion problems for
constant velocities using vectors.
The Big 4
Derivation of Big 4
• See Derivation of Big 4.pdf
• Derivation Notes
What are the Big Ideas of the
Derivation?
Problem Solving
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Step 1: Identify what is given
Step 2: Identify what is asked
Step 3: Select an equation
Step 4: Solve
Step 5: Sig Figs!
Question 1
An airplane accelerates from rest down a runway at
3.20 m/s2 for 32.8 s until is finally lifts off the
ground. Determine the distance traveled before
takeoff.
a = +3.2 m/s2
t = 32.8 s
vi = 0 m/s
Find d = ??
d = (0 m/s)*(32.8 s)+ 0.5*(3.20 m/s2)*(32.8 s)2
d = 1720 m
Question 2
A car starts from rest and accelerates uniformly
over a time of 5.21 seconds for a distance of
110 m. Determine the acceleration of the car.
d = 110 m
t = 5.21 s
vi = 0 m/s
Find:
a = ??
110 m = (0 m/s)*(5.21 s)+ 0.5*(a)*(5.21 s)2
110 m = (13.57 s2)*a
a = (110 m)/(13.57 s2)
a = 8.10 m/s2
a = 8.1 m/s2
Question 3
A race car accelerates uniformly from 18.5 m/s to
46.1 m/s in 2.47 seconds. Determine the
acceleration of the car and the distance traveled.
vi = 18.5 m/s
vf = 46.1 m/s
d = (18.5 m/s+ 46.1 m/s)(0.5)(2.47 s)
d = 79.8 m
t = 2.47 s
Find:
d = ?? a = ??
46.1 m/s = 18.5 m/s + (a)(2.47 s)
a = 11.2 m/s2
2 Part Questions
• Are there other ways to solve?
– Yes, but...
• Don’t use calculated values for 2nd part
questions wherever possible!
– Calculation errors can carry over into later
questions
– Can run into rounding problems if you use
significant figure value
Question 4
A bike accelerates uniformly from rest to a speed of
7.10 m/s over a distance of 35.4 m. Determine
the acceleration of the bike.
vi = 0 m/s
vf = 7.10 m/s
d = 35.4 m
Find:
a = ??
(7.10 m/s2)2 = (0 m/s)2 + 2*(a)*(35.4 m)
a = 0.712 m/s2
Homework
• Big 4 Problems Handout
– Leave out #3
Acceleration due to Gravity
• Acceleration due to gravity on earth: a = -9.8
m/s2
– Use this value in calculations as acceleration
• Acceleration due to gravity is different on
other planets, so watch out for location!
– More to come later
Question 1
Acceleration due to gravity: a = -9.8 m/s2
Upton Chuck is riding the Giant Drop at Great America. If
Upton free falls for 2.6 seconds, what will be his final
velocity and how far will he fall?
a = -9.8 m/s2
t = 2.6 s
vi = 0 m/s
Find:
d = ?? vf = ??
d = (0 m/s)*(2.6 s)+ 0.5*(-9.8 m/s2)*(2.6 s)2
d = 33 m
vf = vi + a*t
vf = 0 + (-9.8 m/s2)*(2.6 s)
vf = -25.5 m/s (- indicates direction)
Question 2
A kangaroo is capable of jumping to a height of 2.62
m. Determine the takeoff speed of the kangaroo.
a = -9.8 m/s2
vf = 0 m/s
d = 2.62 m
Find:
vi = ??
(0 m/s)2 = vi2 + 2*(-9.8 m/s2)*(2.62 m)
vi = 7.17 m/s
Question 3
A feather is dropped on the moon from a height of
1.40 meters. The acceleration of gravity on the
moon is 1.67 m/s2. Determine the time for the
feather to fall to the surface of the moon.
vi = 0 m/s
d = -1.40 m
a = -1.67 m/s2
Find:
t = ??
d = (0 m/s)*(t)+ 0.5*(-1.67 m/s2)*(t)2
t = 1.29 s
Homework
• Physics, Concepts and Conceptions
– P.64 # 1 ,2, 3,
– P.70 #50, 54, 55, 69
• Big 4 Handout
– #3
Interval Questions
• 2 Big 4 questions rolled into 1
• Must be worked out in intervals
– Different accelerations during different phases of
the questions
• What happened during the first acceleration?
What happened during the second
acceleration?
• Very important – Label your intervals clearly!
Question 1
Otto Emissions is driving his car at 25.0 m/s. Otto accelerates at
2.0 m/s2 for 5.00 seconds. Otto then maintains a constant
velocity for 10.0 more seconds. Calculate the total distance
traveled during the entire 15 seconds.
Given:
Interval 1
vi = 25.0 m/s
t = 5.00 s
d = 500. m
a = 2.0 m/s2
Find: d = ??
Interval 2
t = 10.0 s
a = 0.0 m/s2
Find: d = ??
Question 2
Vera Side is speeding down the interstate at 45.0 m/s when she
observes a pileup in the middle of the road. When she first sees the
accident, she is 80.0 m from the pileup. She slows down at a rate of
-10.0 m/s2. Assuming it will take her 0.0500 s to hit the brakes,
determine the distance which Vera Side would travel prior to
reaching a complete stop (if she did not collide with the pileup). Will
Vera hit the cars in the pileup?
Total distance: 104 m
Since the accident pileup is less than 103 m from Vera, she will indeed
hit the pileup before completely stopping (unless she veers aside).
Homework
• Interval Questions handout
2 Object Problems
• 2 different objects, each with its own velocity
and acceleration
• Usually there is one quantity which is shared
by both objects
– Same distance to travel, must catch up with each
other, etc.
• Keep clear which quantities belong to which
object!
• Draw a picture!
Question 1
Fred and his friend Barney are at opposite ends
of a 1.0 km long drag strip. Fred accelerates
from rest toward Barney at 2.0 m/s2. Barney
travels toward Fred at a constant speed of 10
m/s. How much time elapses before Fred and
Barney collide?
t = 27 s
Question 2
Jack, who is running at 6.0 m/s to catch a bus,
sees it start to move when he is 20.0 m away
from it. If the bus accelerates at 1.0 m/s2, will
Jack overtake it? If so, how long will it take
him?
Jack misses the bus!
Homework
• Physics, Concepts and Conceptions
• Pg.75 #66, 67, 68
Relative Motion
• Relative motion occurs when an object
appears to have one motion to one observer
and a different motion to a second observer.
• Observers are moving relative to each other
• Examples:
– Boat crossing a river
– Airplane flying through the air
– 2 cars on the highway
Relative Motion – What to Do?
• Velocity of the object relative to the ground is
equal to the velocity of the object relative to
the medium plus the vector sum of the
velocity of the medium relative to the ground.
• AKA: Vector sums are back!!!!
Question 1
A sports car is travelling east on Highway #1 at
140 km/h and a semi is travelling west on the
same highway at 110 km/h.
a) If you were in the sports car, what is the
apparent velocity of the truck?
250 km/h, W
b) If you were the truck driver, what is the
apparent velocity of the sports car?
250 km/h, E
Question 2
A sports car is travelling east on Highway #1 at 140 km/h
and a semi is travelling east on the same highway at
110 km/h.
a) If you were in the sports car, what is the apparent
velocity of the truck?
30 km/h, W
b) If you were the truck driver, what is the apparent
velocity of the sports car?
30 km/h, E
c) If you are a police office parked at the side of the road,
what is the apparent velocity of both vehicles?
Sports car: 140 km/h, E
Semi: 110 km/h, E
What about Kinematics?
• Kinematics equations (and classical mechanics
in general) are valid for non-inertial reference
frames
• Can’t use if you’re accelerating and observing
motion
Question 3
A boat is crossing a river at 2.00 m/s, N relative
to the water. The river has a current of 2.00
m/s, E relative to the shore. What is the
velocity of the boat relative to the shore?
Homework
• Physics, Concepts and Conceptions
• P. 116 #35, 36,
Review
• Create a foldable highlighting each of the Big 4 Equations!
Outside
Big 4 Equation:
Big 4 Equation:
Big 4 Equation:
Big 4 Equation:
Variables Used:
Inside
Sample Problem & Solution:
Sample Problem & Solution:
Variables Not Present:
Variables Used:
Variables Not Present:
Variables Used:
Variables Not Present:
Sample Problem & Solution:
Sample Problem & Solution:
Variables Used:
Variables Not Present:
Review Continued
• Kinematics Review worksheet
• Relative Motion and Interval Questions
handout
Where Do I Find More Questions?
• Derivations
– Go over derivations!
• General Big 4 Questions
– Big 4 Examples Handout
– Foldable
• Acceleration due to Gravity
– Review Worksheet
• Interval questions
– Relative Motion and Intervals Handout
• 2 Object Problems
– Big 4 Examples Handout #7
– Review worksheet
• Relative Motion
– Relative Motion and Intervals Handout
The plan
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1 – Derivation
2 – Problem Solving & 2 Part Questions
3 - Acceleration due to Gravity
4 – Interval questions
5 – 2 Object Problems
6 – Relative Motion
7 – Review
8 - Test