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# Displacement During Uniform Acceleration

## Evaluate velocity vs time graphs and calculate displacement over time for objects under uniform acceleration

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Falling From Space

### Falling From Space

In 1960, Capt. Joseph Kittinger stepped off the Excelsior platform that was higher than 31 km above the surface of the earth. Capt. Kittinger fell for approximately 4 minutes and 36 seconds, reaching a maximum speed of 614 miles per hour!

#### Why It Matters

• Any object that is dropped near the surface of the earth will accelerate towards the earth. If you were to ignore the effects due to air resistance, every object that is dropped would fall at the same rate. This is known as the acceleration due to gravity and any object that is falling at such a rate is said to be in free fall. By looking at Newton’s 2nd law, we define the weight of an object by the mass of an object multiplied by the acceleration due to gravity on the object.

W=mg\begin{align*}\overrightarrow{W}=m \overrightarrow{g}\end{align*}

• The acceleration due to gravity only acts along the axis which is perpendicular to the surface of the earth. The acceleration due to gravity is another one of the fundamental concepts of classical physics. From objects moving in two dimensions, torque and even work, the concept of free fall and the acceleration due to gravity must be taken into consideration when looking at real world applications.
• Credit: Carla MacNeil
Source: http://www.flickr.com/photos/9363874@N07/1039697905

A bungee jumper accelerates towards earth [Figure2]

#### Can You Apply It?

Using the information provided above, answer the following questions.

1. Why is it ok to ignore air resistance for objects under the influence of gravity for small distance but not large distances?
2. Explain why it is important to consider the acceleration due to gravity of an object that is thrown across a room when you are trying to determine the distance the object will travel.
3. If one were to consider air resistance on an object that is falling, would the velocity of the object be faster or slower when compared to an object that is falling without air resistance?