Applications To Physics [cont.]


GRAVITY AND CONSTANT ACCELERATION

Gravity is the attractive force between any two masses. This force is proportional to the mass of the object, which is why gravity is less on the moon and greater on planets like Jupiter or Neptune.

The acceleration of gravity is constant - 32 feet per second per second or 9.8 meters per second per second, depending on your choice of units.

A conversion into miles per hour is shown below:

Let's drop a ball from a great height and see what happens:

QUESTIONS TO CONSIDER


  1. How fast, in miles per hour, will the object be traveling after 6 seconds? How many feet has it fallen?

  2. Will gravity continue to accelerate this object to an infinite velocity? Why or why not?

  3. Explain the pattern of numbers apparent in each column - use those patterns to complete the table


GRAPHING GRAVITY'S PULL


An acceleration versus time graph would look like this:

The velocity versus time graph would look different:

What does the velocity versus time graph tell us?

**The difference is the same number every time - that means the points form a line when graphed

**This line has a slope - the slope represents the rate of change

**Since the slope of the line doesn't change, the rate of change is a constant

**This constant is the acceleration of gravity

Let's construct a position versus time graph from our table of values:

QUESTIONS TO CONSIDER


  1. How many seconds would an object dropped from 300 feet hit the ground?

  2. At what speed would it be traveling? At what speed in miles per hour?

  3. Suppose a falling object hits the ground at a velocity of 102 ft/sec. - How many seconds had it fallen? From what height was it dropped?


What does the position versus time graph tell us?

**Since the slope each time is increasing, so is the rate of change

**The difference in the slopes is a constant, which means that the rate of change of the rate of change is a constant

**This rate of change of the rate of change is the acceleration of gravity

let's go on to The Mean Value Theorem
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