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