Calculus-Based Physics Introduction
📐 Part 1: Mathematical Foundations
1. Which of the following best describes the relationship between position, velocity, and acceleration in calculus-based physics?
Velocity is the integral of position; acceleration is the integral of velocity
Velocity is the derivative of position; acceleration is the derivative of velocity
Position is the derivative of velocity; velocity is the derivative of acceleration
All three quantities are independent of each other
2. If position is given by x(t) = 3t² + 2t + 1, find the velocity function v(t).
3. Using your answer from question 2, find the acceleration function a(t).
🎯 Part 2: Conceptual Understanding
4. Check all statements that are true about one-dimensional motion:
Displacement can be found by integrating velocity
Velocity is always positive when an object is moving
Acceleration tells us how velocity changes over time
The derivative of acceleration gives us velocity
Position and displacement mean the same thing
5. Explain in your own words why acceleration is the derivative of velocity. What does this mean physically?
📊 Part 3: Graphical Analysis
6. Draw a sketch showing the relationship between position, velocity, and acceleration graphs for an object with constant positive acceleration.
7. If you have a velocity vs. time graph, how would you find:
a) The acceleration: ________________________
b) The displacement: ________________________
🔧 Part 4: Real-World Applications
8. Match each engineering application with the most relevant kinematic concept:
1. Automotive brake design
2. Rocket trajectory planning
3. Elevator speed control
4. Sports equipment design
A. Projectile motion analysis
B. Acceleration and stopping distance
C. Velocity optimization
D. Impact force calculations
9. A car accelerates from rest at 3.5 m/s² for 8 seconds. Calculate:
a) Final velocity: _______________
b) Distance traveled: _______________
🎓 Part 5: Course Preparation & Reflection
10. This course will meet 4 times per week for 7 months. What study strategies will you use to succeed?
Watch instructional videos before each class
Complete practice problems daily
Use solution manuals for self-checking
Keep a tracking chart of completed work
Review previous topics before quizzes
11. What concept from today's lesson challenged you the most? How will you address this challenge?
12. Set three specific goals for your success in this calculus-based physics course:
Goal 1: ________________________________________________
Goal 2: ________________________________________________
Goal 3: ________________________________________________
