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Displacement, Velocity, and Acceleration

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We will use the falling-ball simulation (Background: University of Oregon, n.d.) to calculate the acceleration of gravity on the Earth, Moon, and Mars.

The most general equation for displacement is:
s = s0 + V0t + (1/2)at2

Where:
s = displacement after time t
s0 = initial displacement (location at t = 0)
V0 = initial velocity (velocity at t = 0)
t = elapsed time in seconds
a = acceleration in m/s2
If the object starts at point s0 = 0 with initial velocity V0 = 0, then the equation becomes

s = (1/2)at2

Solving for a in terms of s and t, we get

a = 2s/t2

For a freely falling object in a vacuum, a is the acceleration of gravity, g. If we record the time required for an object to fall a distance s in a time t, we can solve for g. Using the simulation, record the time required for the ball to fall 1, 2, 3, 4, 5, and 6 meters. Organize your results in a table, as follows (the first row has been completed for you). Round numbers to the nearest two decimals.

Answer the following questions.

Why are all the number in the last column approximately the same?
Which of the six trials yields the most accurate estimate for g? Why?
Compare your answer with the accepted value for g. How would you account for the discrepancy, if any?
Repeat the simulation for the Moon and Mars. Record your data in tables, as above. Compare your results with the accepted values for Lunar and Martian gravity (Google "Gravity on other planets.")

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Solution Summary

This solution uses the displacement equation to solve for the acceleration of gravity on the Earth, Moon, and Mars.

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