Notes on using VerticalMotion.xls

This spreadsheet allows students to explore the graphs of acceleration velocity and displacement for a particle which is moving vertically under gravity.

Background: The constant acceleration equations and acceleration due to gravity.

Questions for students:

• What important modelling assumption is being made?
• Why is the graph of the acceleration a horizontal line?
• What does the constant value of the acceleration tell you about the graph of the velocity?
• What does a positive velocity tell you about the vertical height?
• What does a negative velocity tell you about the vertical height?
• What is significant about the point where the velocity becomes zero?
• How could the maximum height be calculated?
• Calculate the maximum height for a particle with an initial velocity of 15 and a starting height of 5. Use the spreadsheet to check.
• For an initial velocity of 16 and a starting height of 4 calculate the time of flight (the time when the vertical height becomes zero).
• For an initial velocity of 20 and a starting height of 6 for how long does the particle have a vertical height of more than 20?
• For an initial velocity of 16 and a starting height of 8 find the area under the velocity time graph up until the point where the velocity is zero. What does this tell you about the vertical height?
• What would happen if you considered the area up until the point where t = 2 instead?
• Try to find general formulae for the maximum height and the time of flight in terms of the initial velocity and starting height taking g = 9.8. Use the spreadsheet to verify your results.