#AP Physics 1: Ultimate Study Guide 🚀

Hey future physicist! 👋 This guide is designed to be your go-to resource for acing the AP Physics 1 exam. Let's break down the key concepts and make sure you're feeling confident and ready to go! Remember, you've got this! 💪

#⚡️ Unit 1: Kinematics

#1.1 Motion in One Dimension

• Displacement vs. Distance:

  • Displacement is the change in position (a vector). 📏
  • Distance is the total path length (a scalar). 🛤️

• Velocity vs. Speed:

  • Velocity is the rate of change of displacement (a vector). 🚗💨
  • Speed is the rate of change of distance (a scalar). 🏃

• Acceleration: The rate of change of velocity. 📈

• Key Equations:

  • $v = \frac{\Delta x}{\Delta t}$ (average velocity)
  • $a = \frac{\Delta v}{\Delta t}$ (average acceleration)
  • Kinematic Equations (for constant acceleration):

    • $v = v_0 + at$

    • $\Delta x = v_0t + \frac{1}{2}at^2$

    • $v^2 = v_0^2 + 2a\Delta x$

#1.2 Motion in Two Dimensions

• Projectile Motion:

  • Horizontal motion has constant velocity (no acceleration). ➡️
  • Vertical motion has constant acceleration due to gravity ($g = 9.8 m/s^2$). ⬇️
  • Analyze horizontal and vertical motion separately. 🧮

• Key Concepts:

  • Initial velocity can be broken into horizontal ($v_{0x} = v_0 \cos\theta$) and vertical ($v_{0y} = v_0 \sin\theta$) components. 📐

  • Time of flight is determined by vertical motion. ⏰

  • Range is determined by horizontal motion. 🎯

#Practice Questions

Practice Question

Multiple Choice:

1. A ball is thrown horizontally from the top of a building with an initial speed of 15 m/s. If the ball hits the ground 2.0 s later, how far horizontally from the base of the building does the ball land? (A) 7.5 m (B) 15 m (C) 30 m (D) 60 m

2. A car accelerates uniformly from rest to a speed of 20 m/s in 5 seconds. What is the average acceleration of the car? (A) 2 m/s² (B) 4 m/s² (C) 5 m/s² (D) 10 m/s²

Free Response:

A projectile is launched from the ground with an initial velocity of 30 m/s at an angle of 60 degrees above the horizontal. Assume air resistance is negligible.

(a) Calculate the initial horizontal and vertical components of the velocity. (2 points) (b) Calculate the time the projectile is in the air. (3 points) (c) Calculate the horizontal distance the projectile travels before hitting the ground. (3 points) (d) Calculate the maximum height the projectile reaches. (2 points)

Answer Key:

Multiple Choice: 1. (C), 2. (B)

Free Response:

(a) $v_{0x} = 30 \cos(60) = 15 m/s$, $v_{0y} = 30 \sin(60) = 26 m/s$ (2 points: 1 for each component) (b) Time to reach max height: 0 = 26 - 9.8t, $t = 2.65 s$. Total time: 2 * 2.65 = 5.3 s (3 points: 1 for using $v_y = 0$ at max height, 1 for correct time to max height, 1 for total time) (c) $x = 15 * 5.3 = 79.5 m$ (3 points: 1 for correct horizontal velocity, 1 for correct time, 1 for correct distance) (d) $v_f^2 = v_i^2 + 2 a \Delta y$, 0 = 26^2 - 2 * 9.8 * \Delta y, $\Delta y = 34.4 m$ (2 points: 1 for correct formula, 1 for correct answer)

#⚖️ Unit 2: Dynamics

#2.1 Forces and Newton's Laws

• Newton's First Law (Inertia): An object at rest stays at rest, and an object in motion stays in motion with the same velocity unless acted upon by a net force. ➡️

• Newton's Second Law: $F_{net} = ma$. The net force on an object is equal to its mass times its acceleration. 💡

• Newton's Third Law: For every action, there is an equal and opposite reaction. ↔️

• Types of Forces:

  • Gravity ($F_g = mg$)

  • Normal Force ($F_N$)

  • Tension ($T$)

  • Friction ($F_f = \mu F_N$)

  • Spring Force ($F_s = -kx$)

#2.2 Free-Body Diagrams (FBDs)

• Draw a dot to represent the object.

• Draw arrows representing all forces acting on the object.

• Label each force with its symbol (e.g., $F_g$, $F_N$, $T$). ✏️

• Choose a coordinate system and resolve forces into components if needed. 📐

#2.3 Applications of Newton's Laws

• Equilibrium: When the net force is zero, the object is in equilibrium (either at rest or moving with constant velocity). ⚖️
• Non-Equilibrium: When the net force is not zero, the object accelerates. 🚀
• Inclined Planes: Resolve forces into components parallel and perpendicular to the plane. ⛰️

#Practice Questions

Practice Question

Multiple Choice:

1. A 10 kg block is pulled across a horizontal surface with a force of 50 N. If the coefficient of kinetic friction between the block and the surface is 0.2, what is the acceleration of the block? (A) 1 m/s² (B) 3 m/s² (C) 5 m/s² (D) 7 m/s²

2. A 2 kg object is suspended from a string....