Ap Physics Unit 1 Progress Check Frq Answers

AP Physics 1 Unit 1 Progress Check: FRQ Answers and In-Depth Explanations

The AP Physics 1 Unit 1 Progress Check, focusing on kinematics, is a crucial assessment. Mastering this unit lays a strong foundation for the entire course. This comprehensive guide will delve into the common types of Free Response Questions (FRQs) encountered in the Unit 1 Progress Check, providing detailed answers and explanations to solidify your understanding. We'll break down the problem-solving strategies and essential concepts you need to succeed.

Understanding the Kinematics Concepts Tested

Before diving into specific FRQs, let's review the core kinematic concepts frequently assessed in Unit 1:

1. Displacement and Distance:

• Displacement (Δx): A vector quantity representing the change in position. It's the straight-line distance between the initial and final positions, with a direction.
• Distance: A scalar quantity representing the total length of the path traveled. It doesn't consider direction.

Key Difference: A car traveling a circular track and returning to its starting point has a total distance traveled but zero displacement.

2. Velocity and Speed:

• Velocity (v): A vector quantity representing the rate of change of displacement. It includes both magnitude (speed) and direction. The formula is: v = Δx/Δt
• Speed: A scalar quantity representing the magnitude of velocity. It's the rate at which distance is covered.

Important Note: Average velocity considers the overall displacement over the entire time interval, while instantaneous velocity describes the velocity at a specific instant.

3. Acceleration:

• Acceleration (a): A vector quantity representing the rate of change of velocity. It indicates how quickly velocity is changing, both in magnitude and direction. The formula is: a = Δv/Δt

Types of Acceleration: Constant acceleration (uniform motion) simplifies calculations significantly. However, the Progress Check may also assess scenarios involving non-constant acceleration, requiring more sophisticated techniques (e.g., using calculus-based methods if covered in your curriculum).

4. Kinematic Equations:

For motion with constant acceleration, the following equations are essential:

• v_f = v_i + at
• Δx = v_i t + ½at²
• v_f² = v_i² + 2aΔx
• Δx = ½(v_i + v_f)t

Where:

• v_i = initial velocity
• v_f = final velocity
• a = acceleration
• t = time
• Δx = displacement

Choosing the appropriate equation depends on the given information and the unknown quantity you need to find.

Example FRQs and Detailed Solutions

Let's analyze some typical FRQ structures and solve them step-by-step.

FRQ Example 1: Motion Along a Straight Line

A car starts from rest and accelerates uniformly at 2 m/s² for 5 seconds. Then it travels at a constant velocity for another 10 seconds before decelerating uniformly to a stop in 3 seconds.

(a) Draw a velocity-time graph representing the car's motion.

(b) Calculate the total displacement of the car.

(c) Determine the average velocity of the car for the entire journey.

Solution:

(a) Velocity-Time Graph:

The graph would consist of three distinct sections:

• Section 1 (0-5s): A straight line with a positive slope representing the uniform acceleration (slope = 2 m/s²). The final velocity at 5 seconds would be v_f = v_i + at = 0 + (2 m/s²)(5s) = 10 m/s.
• Section 2 (5-15s): A horizontal line at 10 m/s representing constant velocity.
• Section 3 (15-18s): A straight line with a negative slope representing uniform deceleration until the velocity reaches 0 m/s. The slope would be (0-10 m/s)/3s = -3.33 m/s².

(b) Total Displacement:

The total displacement is the sum of the displacements during each section:

• Section 1: Δx₁ = v_i t + ½at² = 0 + ½(2 m/s²)(5s)² = 25 m
• Section 2: Δx₂ = vt = (10 m/s)(10s) = 100 m
• Section 3: We can use v_f² = v_i² + 2aΔx. Rearranging for Δx₃: Δx₃ = (v_f² - v_i²)/(2a) = (0 - (10 m/s)²) / (2(-3.33 m/s²)) ≈ 15 m

Therefore, the total displacement is 25 m + 100 m + 15 m = 140 m.

(c) Average Velocity:

Average velocity is the total displacement divided by the total time:

Average velocity = Total displacement / Total time = 140 m / 18 s ≈ 7.78 m/s

FRQ Example 2: Projectile Motion

A ball is thrown horizontally from a cliff 20 meters high with an initial horizontal velocity of 15 m/s. Ignore air resistance.

(a) How long does it take for the ball to hit the ground?

(b) How far from the base of the cliff does the ball land?

(c) What is the ball's final velocity (magnitude and direction) just before it hits the ground?

Solution:

(a) Time to hit the ground:

We can use the vertical motion equation: Δy = v_iy t + ½a_y t²

• Δy = -20 m (negative because it's downward)
• v_iy = 0 m/s (initial vertical velocity is zero since it's thrown horizontally)
• a_y = -9.8 m/s² (acceleration due to gravity)

Solving for t: -20 m = 0 + ½(-9.8 m/s²)t² => t ≈ 2.02 s

(b) Horizontal distance:

The horizontal velocity remains constant (no air resistance). So, the horizontal distance is:

Δx = v_x t = (15 m/s)(2.02 s) ≈ 30.3 m

(c) Final Velocity:

We need to find the final vertical and horizontal velocities separately and then combine them using the Pythagorean theorem.

• Horizontal velocity: Remains constant at 15 m/s.
• Vertical velocity: v_fy = v_iy + a_y t = 0 + (-9.8 m/s²)(2.02 s) ≈ -19.8 m/s

Magnitude of final velocity: √(15² + (-19.8)²) ≈ 24.8 m/s

Direction (angle below the horizontal): θ = tan⁻¹(v_fy / v_fx) = tan⁻¹(-19.8 / 15) ≈ -52.8°

Tips for Success on AP Physics 1 Unit 1 Progress Check

• Thorough Understanding of Concepts: Don't just memorize formulas; understand the underlying physical principles.
• Practice, Practice, Practice: Solve numerous problems of varying difficulty to build your problem-solving skills.
• Diagram and Visualize: Draw diagrams to represent the motion and visualize the problem. This helps in selecting the appropriate equations.
• Units and Significant Figures: Pay close attention to units and use an appropriate number of significant figures in your calculations.
• Check Your Work: Review your solutions for errors in calculations and logic.
• Seek Help When Needed: Don't hesitate to ask your teacher or classmates for clarification on concepts you find challenging.

By mastering these concepts and practicing diligently, you'll significantly improve your performance on the AP Physics 1 Unit 1 Progress Check and build a strong foundation for the rest of the course. Remember, consistent effort and a deep understanding are key to success in AP Physics.