Position, Velocity, and Acceleration
Grace Lewis
8 min read
Study Guide Overview
This study guide covers kinematics in AP Physics 1, focusing on describing motion. Key concepts include frames of reference, position, scalar vs. vector quantities, displacement vs. distance, speed vs. velocity, and acceleration. It also provides exam tips, common question types, and practice questions with a scoring guide covering graph interpretation and vector math.
#AP Physics 1: Motion - The Night Before π
Hey! Let's get you totally prepped for the AP Physics 1 exam. We'll make sure you're confident and ready to go! This guide is designed to be super clear, quick to use, and engaging, so you can make the most of your last-minute review.
#1. Kinematics: Describing Motion
#1.1 Frames of Reference π¨βπ»
Motion is all about how an object's position changes over time, and it's always relative to a frame of reference. Think of it as your point of view. If you're sitting still on a train, you're not moving relative to the train, but you are moving relative to the ground outside.
- Inertial Reference Frame: A frame where Newton's first law holds true (objects at rest stay at rest, objects in motion stay in motion unless acted upon by a force).
Remember, motion is always described relative to something else!
#1.2 Position π
Position is an object's location relative to a fixed point. We often use graphs to visualize this.
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Position vs. Time Graphs:
- Slope = Velocity
- Straight line = Constant velocity
- Curved line = Acceleration
- Zero slope = Object at rest
- Y-intercept = Initial displacement
Caption: A position vs. time graph showing different types of motion. Note the slope indicating velocity.
#1.3 Scalar vs. Vector Quantities π«
Understanding the difference between scalar and vector quantities is crucial. Scalars have magnitude only, while vectors have both magnitude and direction.
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Scalar:
- Magnitude only (e.g., distance, speed, mass, temperature)
- Added/subtracted arithmetically
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Vector:
- Magnitude and direction (e.g., displacement, velocity, acceleration, force)
- Added/subtracted using vector rules
Caption: Visual representation of vectors with different magnitudes.
Vectors have direction, scalars do not. Think of it this way: "Vectors have a 'vibe' (direction), scalars are just 'size' (magnitude)."
#1.4 Displacement vs. Distance π΄ββοΈ
Displacement is the change in position (vector), while distance is the total path length (scalar).
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Displacement (Ξx):
- Vector quantity
- Final position - initial position
- Direction matters (+/- or N/S/E/W)
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Distance:
- Scalar quantity
- Total path traveled
- No direction
Caption: Visual comparison of displacement and distance. The red line is the distance, the blue line is the displacement.
Many students confuse displacement and distance. Remember, displacement is a vector (direction matters), and distance is a scalar (total path).
#1.5 Speed vs. Velocity π
Speed is how fast an object is moving (scalar), while velocity is speed with a direction (vector).
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Speed (s):
- Scalar quantity
- s = distance / time
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Velocity (v):
- Vector quantity
- v = displacement / time
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Velocity vs. Time Graphs:
- Above x-axis = Moving away
- Below x-axis = Moving towards
- Slope = Acceleration
- Zero slope = Constant velocity
- Straight line = Constant acceleration
- Curved line = Changing acceleration
- Area under curve = Displacement
- Y-intercept = Initial velocity
Caption: A velocity vs. time graph showing different types of motion. Note the area representing displacement.
The slope of a position-time graph is velocity, and the slope of a velocity-time graph is acceleration. Remember these relationships!
#Motion Cheat Sheet:
| Velocity | Acceleration | Type of Motion |
|---|---|---|
| V = 0 | A = 0 | At rest |
| V = (+) or (-) | A = 0 | Constant velocity |
| V = (+) | A = (+) | Speeding up |
| V = (-) | A = (-) | Speeding up |
| V = (+) | A = (-) | Slowing down |
| V = (-) | A = (+) | Slowing down |
#1.6 Acceleration π
Acceleration is the rate of change of velocity (vector).
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Average Acceleration (a_avg):
- a_avg = change in velocity / time
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Acceleration vs. Time Graphs:
- Slope = Jerk (rate of change of acceleration)
- Zero slope = Constant acceleration
- Area under curve = Velocity
- Y-intercept = Initial acceleration
Caption: An acceleration vs. time graph showing how acceleration changes over time.
When interpreting graphs, always pay attention to the axes and what the slope and area under the curve represent. This is a common question type!
#2. Final Exam Focus π―
Key Topics: Kinematics graphs (position, velocity, acceleration vs. time), scalar vs. vector quantities, displacement vs. distance, speed vs. velocity, and the relationships between them. These topics are always on the exam!
#2.1 High-Priority Concepts
- Graph Interpretation: Be able to analyze position, velocity, and acceleration vs. time graphs to find displacement, velocity, and acceleration.
- Vector Math: Remember that vector quantities have both magnitude and direction. Use vector addition and subtraction when needed.
- Constant Acceleration: Know the kinematic equations for constant acceleration motion.
#2.2 Common Question Types
- Multiple Choice: Conceptual questions about the differences between scalar and vector quantities, and graph interpretation.
- Free Response: Problems involving motion with constant acceleration, and graph analysis.
#2.3 Last-Minute Tips
- Time Management: Don't spend too much time on one question. If you're stuck, move on and come back later.
- Units: Always include units in your answers, and make sure they are consistent.
- Show Your Work: Even if you get the wrong answer, you can get partial credit if you show your work.
- Stay Calm: Take deep breaths and trust your preparation. You've got this!
#3. Practice Questions
Practice Question
Multiple Choice Questions
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A car travels 20 km east and then 30 km west. What is the total distance traveled and the magnitude of the displacement of the car? (A) 50 km, 10 km (B) 10 km, 50 km (C) 50 km, 50 km (D) 10 km, 10 km
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The slope of a velocity versus time graph represents: (A) displacement (B) speed (C) acceleration (D) distance
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An object is moving with a constant velocity. Which of the following statements is true? (A) The object's acceleration is positive. (B) The object's acceleration is negative. (C) The object's acceleration is zero. (D) The object's speed is changing.
Free Response Question
A toy car moves along a straight track. The carβs velocity as a function of time is shown in the graph below.
(a) Determine the acceleration of the car at t = 2 s.
(b) Calculate the displacement of the car from t = 0 s to t = 5 s.
(c) At what time(s) does the car change direction?
(d) Sketch a qualitative graph of the carβs position as a function of time from t = 0 s to t = 5 s.
Scoring Guide
(a) 2 points
- 1 point for finding the slope of the line between t=1 and t=3 seconds
- 1 point for correct answer of 2 m/s^2
(b) 3 points
- 1 point for using the correct method of finding the area under the curve
- 1 point for correctly finding the area between 0 and 3 seconds
- 1 point for correctly finding the area between 3 and 5 seconds and calculating the total displacement of 13 meters
(c) 1 point
- 1 point for correctly identifying t = 3 seconds
(d) 3 points
- 1 point for correctly showing an increasing slope between 0 and 3 seconds
- 1 point for correctly showing a decreasing slope between 3 and 5 seconds
- 1 point for correctly showing a continuous graph
Remember, you've got this! Go ace that exam! πͺ
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