# The four kinematic equations which describe an object's motion are: - PowerPoint PPT Presentation

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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.

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

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### 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.

### 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

### 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.

### 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

### 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.

### 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.

### 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.

### 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

### 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.

### 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