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

There are a variety of symbols used in the above equations and each symbol There are a variety of symbols used in the above equations and each symbol has a specific meaning. has a specific meaning.

d – the displacement of the object. d – the displacement of the object. (we use “x” & will also use “y”)(we use “x” & will also use “y”) t – the time for which the object moved.t – the time for which the object moved. a – the acceleration of the object.a – the acceleration of the object. vvii – the initial velocity of the object. – the initial velocity of the object. vvff – the final velocity of the object. – the final velocity of the object.

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

Position Of Free Falling Object Position Of Free Falling Object At Regular Time IntervalsAt Regular Time Intervals

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

Velocity Of Free Falling Object At Velocity Of Free Falling Object At Regular Time IntervalsRegular Time Intervals

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

Velocity Of Free Falling Object At Velocity Of Free Falling Object At Regular Time IntervalsRegular Time Intervals

Observe that the line on the graph is curved. Observe that the line on the graph is curved. A curved line on a position vs. time graph signifies an accelerated motion. signifies an accelerated motion. Since a free-falling object is undergoing an acceleration of g = 10 m/s/s 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 (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 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). 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, 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 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 slope indicates a large final velocity. Last, but not least, the negative slope of the line indicates a negative (i.e., downward) velocity.of the line indicates a negative (i.e., downward) velocity.

Velocity Of Free Falling Object At Velocity Of Free Falling Object At Regular Time IntervalsRegular Time Intervals

look at the velocity-time graph reveals that the object starts with a look at the velocity-time graph reveals that the object starts with a zero velocity (starts from rest) and finishes with a large, negative zero velocity (starts from rest) and finishes with a large, negative velocity; that is, the object is moving in the negative direction and 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. An object which is moving in the negative direction and speeding up is said to have a negative accelerationspeeding up is said to have a negative acceleration

This analysis of the slope on the graph is consistent with the This analysis of the slope on the graph is consistent with the motion of a free-falling object – an object moving with a constant motion of a free-falling object – an object moving with a constant

acceleration of 10 m/s/s in the downward direction.acceleration of 10 m/s/s in the downward direction.

How Fast?How Fast? The velocity of a free-falling object The velocity of a free-falling object

which has been dropped from a which has been dropped from a position of rest is dependent upon the position of rest is dependent upon the length of time for which it has fallen. length of time for which it has fallen. The formula for determining the The formula for determining the velocity of a falling object after a time velocity of a falling object after a time of t seconds is: of t seconds is:

vvff = v = vii + (-g)t + (-g)t

where where gg is the acceleration of gravity is the acceleration of gravity (approximately -10 m/s/s on Earth; its (approximately -10 m/s/s on Earth; its exact value is -9.81 m/s/sexact value is -9.81 m/s/s). The ). The equation above can be used to equation above can be used to calculate the velocity of the object calculate the velocity of the object after a given amount of time.after a given amount of time.

How FAST ? ExampleHow FAST ? Example t = 6 s t = 6 s

vvff = (0 m/s) + (-10 m/s = (0 m/s) + (-10 m/s22) (6 s) = ) (6 s) = - 60 m/s- 60 m/s

t = 8 st = 8 s

vvff = (0 m/s) + (-10 m/s = (0 m/s) + (-10 m/s22)(8 s) = )(8 s) = - 80 m/s- 80 m/s

How Far?How Far?

How FAR ? ExampleHow FAR ? Example

The NEGATIVE displacement, indicates that the object is falling DOWN