The four kinematic equations which describe an object's motion are:

1
The four kinematic equations which describe an
object's motion are

• There are a variety of symbols used in the above
  equations and each symbol has a specific meaning.
  
• d the displacement of the object. (we use x
  will also use y)
• t the time for which the object moved.
• a the acceleration of the object.
• vi the initial velocity of the object.
• vf the final velocity of the object.

2
The four kinematic equations which describe an
object's motion are

• If there is NO AIR RESISTANCE ALL objects,
  regardless of weight size, will fall at the
  same acceleration.
• The Acceleration of gravity
• g -9.81 m/s/s

3
Position Of Free Falling Object At Regular Time
Intervals

• The position of the free-falling object at
  regular time intervals, every 1 second, is shown.
  The fact that the distance which the ball travels
  every interval of time is increasing is a sure
  sign that the ball is speeding up as it falls
  downward.

4
Velocity Of Free Falling Object At Regular Time
Intervals

• Assuming that the position of a free-falling ball
  dropped from a position of rest is shown every 1
  second, the velocity of the ball will be shown to
  increase

5
Velocity Of Free Falling Object At Regular Time
Intervals

• Observe that the line on the graph is curved. A
  curved line on a position vs. time graph
  signifies an accelerated motion. Since a
  free-falling object is undergoing an acceleration
  of g 10 m/s/s (approximate value), you would
  expect that its position-time graph would be
  curved. A closer look at the position-time graph
  reveals that the object starts with a small
  velocity (slow) and finishes with a large
  velocity (fast). Since the slope of any position
  vs. time graph is the velocity of the object, the
  initial small slope indicates a small initial
  velocity and the final large slope indicates a
  large final velocity. Last, but not least, the
  negative slope of the line indicates a negative
  (i.e., downward) velocity.

6
Velocity Of Free Falling Object At Regular Time
Intervals

• look at the velocity-time graph reveals that the
  object starts with a zero velocity (starts from
  rest) and finishes with a large, negative
  velocity that is, the object is moving in the
  negative direction and speeding up. An object
  which is moving in the negative direction and
  speeding up is said to have a negative
  acceleration
• This analysis of the slope on the graph is
  consistent with the motion of a free-falling
  object an object moving with a constant
  acceleration of 10 m/s/s in the downward
  direction.

7
How Fast?

• The velocity of a free-falling object which has
  been dropped from a position of rest is dependent
  upon the length of time for which it has fallen.
  The formula for determining the velocity of a
  falling object after a time of t seconds is
• vf vi gt
• where g is the acceleration of gravity
  (approximately -10 m/s/s on Earth its exact
  value is -9.81 m/s/s). The equation above can be
  used to calculate the velocity of the object
  after a given amount of time.

8
How FAST ? Example

• t 6 s
• vf (0 m/s) (10 m/s2) (6 s) 60 m/s
• t 8 s
• vf (0 m/s) (10 m/s2)(8 s) 80 m/s

9
How Far?

• The distance which a free-falling object has
  fallen from a position of rest is also dependent
  upon the time of fall. The distance fallen after
  a time of t seconds is given by the formula
  below
• x (1/2) g t2
• where g is the acceleration of gravity
  (approximately -10 m/s/s on Earth its exact
  value is -9.81 m/s/s). The equation above can be
  used to calculate the distance traveled by the
  object after a given amount of time.

10
How FAR ? Example

• t 1 s
• x (1/2) (-10 m/s2) (1 s)2 -5 m
• t 2 s
• x (1/2) (-10 m/s2) (2 s)2 -20 m
• t 5 s
• x (1/2) (-10 m/s2) (5 s)2 -125 m

The NEGATIVE displacement, indicates that the
object is falling DOWN