A Summary of Motion

1
A Summary of Motion

• Measurements, Graphs and Equations

2
Scalars and Vectors

• Scalar quantities are measurements that have no
  statement of direction.
• Vector quantities are measurements that have a
  statement of direction.
• Direction can be forward or backwards, indicated
  by or - , or it can be compass points such as
  N, S, E, or W. Up and down are also directions

3
Position

• Position is the location of an object based on a
  reference point. Often, though not always, the
  reference point is assigned a zero value.
• A reference point does not have to be zero, it
  can be any point the author of a problem decides
  it should be.
• The starting point in a motion problem does not
  have to be the reference point.

4
Displacement

• Displacement is a measure of an objects change
  in position.
• Displacement is usually measured in a straight
  line from the start position to the end position
  of the motion.
• Displacement has a direction associated with it.
  This could be forward vs reverse, or north vs
  south, or east vs west, or up vs down.

5
Speed

• Speed is a statement about how fast an object is
  traveling.
• Speed measures the rate of change between
  distance and time.
• Speed has no statement of direction.
• Speed is found by dividing the total distance
  traveled by an object by the time interval during
  which the object moved.
• Speed is the magnitude of an objects velocity
• Speed has a number and a unit i.e. 5 m/s

6
Velocity

• Velocity is a statement about how fast an object
  is going plus the direction it is going.
• Velocity measures the rate of change between
  displacement and time.
• Velocity has a statement of direction.
• Velocity is found by dividing the displacement of
  an object by the time interval during which the
  object moved.
• Velocitys magnitude is speed
• Velocity has a number, a unit, and direction
  i.e. 5 m/s, E

7
Acceleration

• Acceleration is a statement about how fast an
  objects velocity changes.
• Acceleration measures the rate of change between
  velocity and time.
• Acceleration has a statement of direction.
• Acceleration is found by dividing the change in
  velocity of an object by the time interval during
  which the velocity changed.
• Acceleration has a number, a unit, and direction
  i.e. 9.8 m/s2, N

8
Constant velocity (uniform motion)

• Constant velocity is a situation where an object
  moves along with a constant change in its
  position.
• On the right youll see a typical position-time
  graph where the velocity is constant.

Position vs Time
9
Constant Velocity (uniform motion)

• Constant velocity is a situation where an object
  moves along with a constant change in its
  position.
• On the right youll see a typical velocity-time
  graph where the velocity is constant

Velocity vs Time
10
Uniform (constant) Acceleration

• Uniform or constant acceleration is a situation
  where an object moves along with a constant
  change in its velocity.
• On the right youll see a typical position-time
  graph where the acceleration is constant

Position vs Time
11
Uniform (constant) Acceleration

• Uniform or constant acceleration is a situation
  where an object moves along with a constant
  change in its velocity.
• On the right youll see a typical velocity-time
  graph where the acceleration is constant

Velocity vs Time
12
Falling Bodies and Acceleration

• According to the Law of Gravity, all objects fall
  with the same rate of acceleration when they are
  in free fall.
• Free fall is a situation where air friction has
  no effect on the falling body.
• On earth (only) the average rate of downwards
  acceleration g is 9.8 m/s2

13
Summary

• We have looked at three generic scenarios.
• 1. Constant velocity
• 2. Acceleration in a horizontal direction
• 3. Acceleration in a vertical direction free
  fall
• For further review it is strongly recommended
  that you go to your text references and read,
  study, and take notes on the example and the
  practice problems in your textbook.

14
Acceleration due to Gravity

• Uniform acceleration of gravity is a situation
  where an object falls along with a constant
  change in its velocity.
• On the right youll see a typical position-time
  graph where an object accelerates downwards.

Position vs Time
15
Acceleration due to Gravity

• Uniform acceleration of gravity is a situation
  where an object falls along with a constant
  change in its velocity
• On the right youll see a typical velocity-time
  graph where an object accelerates downwards.

Velocity vs Time
16
Time clock time and time interval

• Time can be thought of in one of two ways. It can
  be an exact time as in What time is it right
  now? or it can represent a period of time often
  referred to as the duration of an event.
• t or Clock time is what it says on a clock, etc.
• /\t t(f) t(i) is the difference between two
  clock times and is often referred to as the
  duration of an event.

17
Distance and Speed

• Distance or what is often called total distance
  is not the same as displacement. It is simply the
  total of all of the distances an object travels
  in a time interval
• Speed is simply equal to the total of all of the
  distances divided by the time interval.
• Equation Speed d(total) / /\t

18
Equations for Constant velocity

• Constant velocity velocity that remains the same
  during the time interval an ojects motion is
  being studied or observed.
• /\d d(f) d(i) often d(i) 0 m, km, mi,
  etc., so /\d is simply d(f) or d(total)
• V(ave) /\d / /\t
• /\d V(ave) /\t
• /\t /\d / V(ave)

19
Equations for Uniform Acceleration

• Uniform acceleration The situation where the
  velocity continuously changes by the same amount
  of velocity each second, thus causing position to
  change by an ever increasing amounts per unit of
  time (i.e. per second)
• a(ave) /\v / /\t where /\v v(f) v(i)
• d(f) d(i) 0.5 vi vf / 2 /\t
• d(f) v(i) /\t 0.5 a /\t2
• v(f) v(i) a t
• v(f)2 v(i)2 2 a /\d

20
Equations for Uniform Acceleration during free
fall. (g a 9.8 m/s2)

• Uniform acceleration The situation where the
  velocity continuously changes by the same amount
  of velocity each second, thus causing position to
  change by an ever increasing amounts per unit of
  time (i.e. per second)
• g(ave) /\v / /\t where /\v v(f) v(i)
• d(f) d(i) 0.5 v(i) v(f) / 2 /\t
• d(f) v(i) /\t 0.5 g /\t2
• v(f) v(i) g /\t
• vf2 vi2 2 g /\d