Gravity Trails Presentation
Gravity Trails
Visualizing Motion Under Constant Acceleration
9th Grade Physical Science
Warm-up
5 Minutes | Thinking in Graphs
On your lab sheet, sketch a Position vs. Time graph for a car moving at a constant speed.
Consider:
- What is on the y-axis?
- What is on the x-axis?
- Is the slope straight or curved?
The Invisible Pull
Embedded media
Watch 0:00 - 0:50: The Apple Drop & Gravitational Acceleration
Gravity is an...
Accelerating Force
Key Value:
\( g = 9.8 \text{ m/s}^2 \)
Downwards Direction
Problem: The Cliff Toss
Problem 3
A rock is thrown straight up from a cliff at 13 m/s.
The Variables
Initial Velocity (\( v_i \))
+13 m/s
Gravity (\( g \))
9.8 m/s²
Position (d) vs Time (t)
The Prediction Tool
Kinematic Equation for Vertical Motion
Final Position Formula
\[ d_f = v_i t - \frac{1}{2} g t^2 \]
\( v_i \)
13 m/s
\( t \)
0, 1, 2, 3 sec
\( g \)
9.8 m/s²
Graphing Gravity
1
Calculate
Find the rock's position at \( t = 0, 1, 2, \text{ and } 3 \) seconds.
2
Plot
Map your data points onto the Position vs. Time graph on your sheet.
3
Connect
Draw a smooth curve connecting the points.
Use Your Rulers
The Extension
Where will it be at the next tick?
Predict at t = 4 seconds
- Calculate the exact position using the equation.
- Plot the point and extend your curve.
Gravity Trails Lab Sheet
Gravity Trails
9th Grade Physical Science | Kinematics Lab
Name:
Date:
Part 1: Warm-up Sketch
Sketch a Position vs. Time graph for an object moving at a constant speed. Label your axes.
Time (s)
Position (m)
Part 2: The Cliff Toss Data
Scenario: Problem 3
A rock is thrown straight up from a cliff with an initial velocity (\(v_i\)) of 13 m/s. Calculate its position (\(d_f\)) at each time using the formula below.
\[ d_f = (13)t - \frac{1}{2}(9.8)t^2 \]
| Time (s) | Calculation Space | Position (m) |
|---|
| t = 0 | \( 13(0) - 4.9(0)^2 \) | 0.0 m |
| t = 1 | | |
| t = 2 | | |
| t = 3 | | |
| | |
| t = 4 Extension | | |
| | |
Part 3: Visualization Path
+15
+10
+5
0
-5
-10
-15
-20
-25
-30
-35
1.0 s
2.0 s
3.0 s
4.0 s
Position (meters)
Time (seconds)
Mapping Instructions
Plot your results for \( t = 0, 1, 2, \) and \( 3 \). If you finished the extension, plot \( t = 4 \) as well. Connect the dots with a smooth, curved line. Do not use straight segments!
Gravity Trails Teacher Guide
Teacher Resource
Gravity Trails
Instructional Guide & Answer Key
Lesson Objective
Students will calculate and graph the vertical displacement of a projectile under the constant acceleration of gravity (\(g\)). By the end of the lesson, students should recognize that motion under constant acceleration creates a parabolic (curved) path on a Position vs. Time graph, unlike the linear path of constant velocity.
Lesson Pacing
- Warm-up 5 min
- Video & Intro 10 min
- Activity 25 min
- Discussion 5 min
Instructional Keys
Sign Convention
Remind students that upward is positive (+) and gravity is negative (-) because it acts downward. This is why the equation uses \(- \frac{1}{2}gt^2\).
The Parabola
Highlight the difference between the linear warm-up graph (constant speed) and this curved graph (changing speed/acceleration).
Video Segment Note
The video mentions Problem 3 at the 9:35 mark. If students get stuck on calculations, refer them to the methodology shown in the video.
Common Pitfalls
Students often forget to square the time (\(t^2\)) or treat gravity as a positive number in the calculation, which will result in the rock flying upward forever.
Answer Key
Calculation Results
t = 0 s
d = 0.0 m
t = 1 s
\( 13(1) - 4.9(1)^2 = 13 - 4.9 \)
d = 8.1 m
t = 2 s
\( 13(2) - 4.9(2)^2 = 26 - 19.6 \)
d = 6.4 m
t = 3 s
\( 13(3) - 4.9(3)^2 = 39 - 44.1 \)
d = -5.1 m
t = 4 s (Extension)
\( 13(4) - 4.9(16) = 52 - 78.4 \)
d = -26.4 m
Graph Profile
Conceptual Path Only
The "Turn-around" Point
The rock reaches its peak between 1.0 and 2.0 seconds. On the graph, this is the "hump" where the slope becomes zero before becoming negative. This signifies the moment the rock stops moving up and starts falling down.
Exit Discussion
Question 1
Why did the rock eventually end up at a negative position?
Answer: Because the displacement final is measured from the release point (cliff top). Negative means it fell below the level of the person's hand.
Question 2
Does the mass of the rock change this graph?
Answer: No. As demonstrated in the Galileo and bowling ball vs. feather examples, acceleration due to gravity is independent of mass (ignoring air resistance).
