Kinematics Review

1
Kinematics Review

• SPH4U Grade 12 Physics
• Unit 3

2
Review - Motion

• The study of motion is called kinematics.
• In physics we study scalar and vector quantities.
  
• Scalar quantities do not have a direction.
• Ex. Speed 2 km/hr
• Vector quantities have both a magnitude and a
  direction. Ex. Velocity 3 m/s South

3
Review - Motion

• Position is the distance with a direction from
  some reference point.
• Displacement is the change is position.
• Velocity is the rate of change of displacement.
• Instantaneous velocity is the velocity at a
  particular instant in time. It is found by
  finding the slope of the tangent at that point to
  a displacement-time graph.

4
Uniform Motion

• Recall Uniform motion is movement in a straight
  line at a constant speed.
• Most motion is non-uniform.
• The position-time graph for uniform motion will
  be a straight line with a positive slope.

5
Review Motion Graphs

• On a displacement time graph (p-t) or (d-t), the
  slope represents velocity.

6
Uniform Motion

• Non-uniform motion, by default, is accelerated
  motion. Accelerated motion occurs when we have a
  change in speed or direction or both.
• Uniformly accelerated motion is when an object is
  travelling in a straight line and changes its
  speed uniformly with time.

7
Uniform Motion

• Uniformly accelerated motion (also known as
  uniform acceleration) will have a straight line
  on a v-t graph and a flat straight line on an a-t
  graph.
• In this course, we only examine things that
  have uniform acceleration.

8
Uniform Motion

• Uniformly accelerated motion

9
Review Motion Graphs

• On a v-t graph, the slope represents acceleration
  because acceleration is the rate of change of
  velocity.

10
Practice

• 1) In the graph below, explain what is happening
  to the objects motion for each time interval.

11
Practice

• 1) In the graph below, explain what is happening
  to the objects motion for each time interval.

Not moving
Constant velocity Away from origin
Constant velocity toward origin
Accelerating away from origin
12
Practice

• 2) Using the p-t graph given, construct the v-t
  graph. Determine the average velocity between 0
  and 6 seconds. Determine the instantaneous
  velocity at 3 seconds.

13
Practice

• 2) Using the p-t graph given, construct the v-t
  graph. Determine the average velocity between 0
  and 6 seconds. Determine the instantaneous
  velocity at 3 seconds.

Average velocity 5/6 m/s
0.83 m/s Inst. Velocity slope of
straight line 1 m/s
v-t graph
1
velocity (m/s)
0
-2
time (s)
14
Practice

• 3) Using the v-t graph given, sketch the a-t
  graph.

15
Practice

• 3) Using the v-t graph given, sketch the a-t
  graph.

a-t graph
6
2.6
Acceleration (m/s2)
0
-4
time (s)
16
Review Equations of Motion

• Recall the following important equations of
  motion (you can find these in Table 1 on pg. 18)

17
Practice

• 4) A man starts from rest and then runs north
  with a constant acceleration. He travels 120m in
  15 seconds. Calculate his acceleration.

18
Practice

• 4) A man starts from rest and then runs north
  with a constant acceleration. He travels 120m in
  15 seconds. Calculate his acceleration.

19
Review Free Fall

• Free fall is the motion of an object falling to
  the earths surface with no other force acting on
  it other than gravity.
• The average acceleration on the Earth due to the
  Earths force of gravity is . This is also
  called the gravitational field intensity.

20
Review Projectiles

• Projectile motion is motion with a constant
  horizontal velocity combined with a constant
  vertical acceleration caused by gravity.
• A projectile is an object that moves through the
  air, along a trajectory without a propulsion
  system.

21
Review Projectiles

• Recall the following equations that are useful
  for projectile problems

22
Practice

• 5) A projectile is launched with an initial speed
  of 14.5 m/s at an angle of 35.0º above the
  horizontal. The object lands at the same height
  from which it was launched. What is the
  projectiles maximum height?

23
Practice

• 5) A projectile is launched with an initial speed
  of 14.5 m/s at an angle of 35.0º above the
  horizontal. The object lands at the same height
  from which it was launched. What is the
  projectiles maximum height?

24
Relative Motion

• When we observe motion, we are always measuring
  it with reference to some particular frame.
  Relative motion is motion observed from a
  specific perspective or frame of reference.
• The velocity of an object relative to a specific
  frame of reference is called relative velocity.

25
Relative Motion

• We can solve relative velocity questions using
  the following equation
• velocity of A moving relative to C
• velocity of A moving relative to B
• velocity of B moving relative to C

 
 
 
 
26
Example

• Suppose the school bus moves at a velocity of 40
  km/h E, relative to the ground. A student
  rolls an apple down the middle of the bus at a
  velocity of 2 km/h E relative to the student.
• What is the velocity of the ball relative to the
  ground?

27
Example

• Suppose the school bus moves at a velocity of 40
  km/h E, relative to the ground. A student
  rolls an apple down the middle of the bus at a
  velocity of 2 km/h E relative to the student.
• What is the velocity of the ball relative to the
  ground?
• velocity of the bus moving
  relative to the ground
• velocity of the apple moving
  relative to the bus
• velocity of the apple moving relative to
  the ground

 
 
 
 
28
Example

• Suppose the school bus moves at a velocity of 40
  km/h E, relative to the ground. A student
  rolls an apple down the middle of the bus at a
  velocity of 2 km/h E relative to the student.
• What is the velocity of the ball relative to the
  ground?
• 40 km/h E
• 2 km/h E
• ?

 
 
 
 
 
 
29
Practice

• 6) A child rolls a ball across a boat at a
  velocity of 4 m/s N (relative to the boat). If
  the boat is travelling at 6m/s W relative to
  the shore, what is the velocity of the ball
  relative to the shore?

30
Practice

• 6) A child rolls a ball across a boat at a
  velocity of 4 m/s N (relative to the boat). If
  the boat is travelling at 6m/s W relative to
  the shore, what is the velocity of the ball
  relative to the shore?
• vbB 4m/s N vbs vbB vBs
• vBs 6m/s W vbs 4 N
  6 W
• (use pathagorean theorem)
• vbs 7.2 N 56º W
• vbs ?

31
Homework

• Read sections 1.1 -1.6. Supplement your notes
  with these readings.
• Complete the Self-Quiz on page. 53
• On pg. 55 Answer Questions 36, 38, 48, 54, 55,
  59, 67, 75, 77