Physics Study Notes: Displacement, Speed, and Acceleration
Objective Overview
Discuss displacement and speed.
Practice using speed equations for word problems.
Reminders:
Quiz corrections scheduled for Thursday from 4:00 to 4:30.
Office/student hours are on Monday and Thursday from 4:00 to 4:30.
Kinematics
Motion in One Dimension
Key Concepts
Displacement, Velocity, and Acceleration
Displacement
Definition: Change in position of an object.
Can be positive or negative.
Displacement is not always equal to the distance traveled.
Average Velocity
Formula: Average Velocity = Displacement / Time.
Can be positive or negative.
Important distinctions:
Not the same as speed (where Speed = Distance / Time).
Not the same as instantaneous velocity (which accounts for speed at a specific moment).
### Acceleration
Definition: Rate of change in velocity.
Can be positive or negative.
Indicates change in speed, direction, or both.
Formula: Acceleration = Change in Velocity / Change in Time.
Sample Problems
Average Speed
Sample Problem 1: A kingfisher dives from a height of 7.0 m with an average speed of 4.00 m/s. To find the time taken to reach the water:
Use formula: Time = Distance / Speed.
Calculation: Time = 7.0 m / 4.00 m/s = 1.75 s.
Sample Problem 2: Riding a bicycle:
You ride 1 km at 10 km/h and another 1 km at 30 km/h. To determine the average speed over 2 km:
Total distance = 2 km.
Total time = (1 km / 10 km/h) + (1 km / 30 km/h).
Calculate each section:
Time1 = 0.1 hr, Time2 = 0.033 hr.
Total time = 0.1 + 0.033 = 0.133 hr.
Average speed = Total Distance / Total Time = 2 km / 0.133 hr = 15.03 km/h (which is less than 20 km/h).
Average Velocity
Sample Problem: A skateboarder with an initial position of 1.5 m moves with a constant velocity of 3.0 m/s. To find the position at t = 2.5 s:
Final Position = Initial Position + (Velocity x Time).
Final Position = 1.5 m + (3.0 m/s x 2.5 s) = 1.5 + 7.5 = 9.0 m.
Further Objectives
Discuss acceleration and practice using acceleration equations for word problems.
Understanding Acceleration
Application of Concepts
Calculation of average acceleration example problems:
Problem 1: A shuttle bus slows down with an average acceleration of -1.8 m/s². Calculating time to slow from 9.0 m/s to a complete stop:
Final velocity (vf) = 0 m/s.
Initial velocity (vi) = 9.0 m/s.
Acceleration (a) = -1.8 m/s².
Applying the first kinematic equation: vf = vi + at = 0 = 9.0 - 1.8t.
Rearranging gives us t = 9.0 / 1.8 = 5.0 s.
Problem 2: A greyhound running from rest accelerates at 9 m/s² to reach a speed of 24 m/s:
Use the equation: vf = vi + at, meaning 24 = 0 + 9t, solving gives t = 24 / 9 = 2.67 s.
Problem 3: Calculating acceleration from rest, reaching 8 m/s in 3 seconds:
Acceleration = (vf - vi) / t = (8 - 0) / 3 = 2.67 m/s².
Problem 4: A car starts from rest, accelerates at 0.5 m/s² for 5 seconds:
Use vf = vi + at = 0 + 0.5 * 5 = 2.5 m/s as final velocity.
Lab Objectives
Measuring Student Velocity
The class measures the time taken for multiple students to move 50 meters.
Data is collected to analyze average speeds through trials.
Procedure:
Mark 10 m intervals using sidewalk chalk or tape.
Position timers at every mark (total 6 positions).
Collect the data based on when students pass each mark.
Record average times rounded to the nearest tenth.
Data Collection Structure:
Mover A performance:
Walk from 0 to 50 m, Average Time (s).
Mover B performance:
Jog from -20 to 50 m, Average Time (s).
Mover C performance:
Walk back from 50 m to 0, Average Time (s).
Mover D performance:
Accelerate consistently, Average Time (s).
Graphing Strategy:
Graph Position vs. Time and Velocity vs. Time.
Analyze trends: Slope indicates speed; a steep slope indicates high speed, while a flat line denotes no speed.