Grade: Grade 11 Subject: Science Unit: Physics Lesson: 6 of 6 SAT: ProblemSolving+DataAnalysis ACT: Science

Unit Checkpoint

Unit Overview

This checkpoint assesses your understanding of the key concepts covered in the Physics unit. Before attempting the assessment, review the main topics from each lesson:

Lesson 1: Mechanics

  • Kinematics: displacement, velocity, acceleration
  • Newton's Three Laws of Motion
  • Free fall and projectile motion
  • Forces: gravity, friction, normal force, tension

Lesson 2: Energy and Work

  • Work = Force x Distance x cos(theta)
  • Kinetic energy: KE = (1/2)mv^2
  • Potential energy: PE = mgh (gravitational), PE = (1/2)kx^2 (elastic)
  • Conservation of energy
  • Power = Work / Time

Lesson 3: Investigation Lab

  • Scientific method in physics
  • Independent, dependent, and controlled variables
  • Measurement uncertainty and error analysis
  • Percent error calculations

Lesson 4: Data and Graphs

  • Organizing data in tables
  • Position-time, velocity-time, and force-acceleration graphs
  • Slope and area interpretations
  • Linearizing non-linear relationships

Lesson 5: CER Writing

  • Claim-Evidence-Reasoning structure
  • Writing specific, testable claims
  • Using quantitative evidence
  • Connecting evidence to scientific principles

Review Examples

Integrated Example 1: Motion Analysis

Problem: A 2.0 kg object starts from rest and accelerates uniformly down a frictionless 30-degree incline that is 5.0 m long. Find: (a) the acceleration, (b) the final velocity, (c) the time to reach the bottom.

Solution:

(a) Acceleration: a = g sin(30) = 9.8 x 0.5 = 4.9 m/s^2

(b) Using energy: mgh = (1/2)mv^2, where h = 5.0 x sin(30) = 2.5 m

v = sqrt(2gh) = sqrt(2 x 9.8 x 2.5) = sqrt(49) = 7.0 m/s

(c) Using v = at: t = v/a = 7.0/4.9 = 1.43 s

Integrated Example 2: Experimental Design

Scenario: Design an experiment to verify that kinetic energy depends on the square of velocity.

Approach:

  • Independent variable: velocity (vary by changing ramp height)
  • Dependent variable: kinetic energy (calculate from 1/2 mv^2)
  • Controlled: mass, ramp surface, release technique
  • Graph: Plot KE vs. v (expect parabola) or KE vs. v^2 (expect straight line through origin)
  • The slope of KE vs. v^2 should equal (1/2)m

Checkpoint Assessment

Complete all problems to assess your understanding of the Physics unit.

Part A: Mechanics (Problems 1-3)

1. A car accelerates from 15 m/s to 35 m/s in 4.0 seconds. Calculate (a) the acceleration and (b) the distance traveled during this time.

2. A 5.0 kg box is pushed across a floor with a horizontal force of 40 N. If the coefficient of kinetic friction is 0.3, calculate the acceleration of the box.

3. A projectile is launched horizontally at 15 m/s from a cliff 80 m high. Calculate (a) the time of flight and (b) the horizontal distance traveled.

Part B: Energy and Work (Problems 4-5)

4. A 1200 kg car traveling at 20 m/s comes to a stop over a distance of 50 m. Calculate (a) the initial kinetic energy, (b) the work done by the brakes, and (c) the average braking force.

5. A spring with k = 500 N/m is compressed 0.15 m and releases a 0.2 kg ball. Using conservation of energy, calculate the maximum speed of the ball.

Part C: Investigation Skills (Problems 6-7)

6. A student measures the period of a pendulum as 1.82 s, 1.79 s, 1.85 s, 1.80 s, and 1.84 s. Calculate (a) the mean period, (b) the range, and (c) the uncertainty in the measurement.

7. An experiment predicts that an object will fall 4.9 m in 1.0 s. The actual measured distance is 4.5 m. Calculate the percent error and identify one possible source of systematic error.

Part D: Data Analysis (Problems 8-9)

8. A velocity-time graph shows a straight line from (0 s, 5 m/s) to (8 s, 25 m/s). Calculate (a) the acceleration and (b) the total displacement represented by the area under the graph.

9. The following data shows the relationship between the period T of a pendulum and its length L:
L (m): 0.25, 0.50, 0.75, 1.00
T (s): 1.00, 1.41, 1.73, 2.00
What graph would you plot to obtain a linear relationship, and what would the slope tell you?

Part E: Scientific Writing (Problems 10-12)

10. Write a claim that answers the question: "How does doubling the mass of a cart affect its kinetic energy if velocity is held constant?"

11. Using the following data, write an evidence statement for a momentum conservation experiment:
Before collision: Cart A (0.5 kg at 4.0 m/s), Cart B (0.5 kg at rest)
After collision: Both carts stuck together moving at 2.1 m/s

12. Write a complete CER response for the following question and data:
Question: Does the acceleration of an object depend on the net force applied?
Data (for a 1.5 kg cart): Force 3.0 N = acceleration 2.0 m/s^2; Force 6.0 N = acceleration 4.0 m/s^2; Force 9.0 N = acceleration 6.0 m/s^2

Self-Assessment Rubric

Use this rubric to evaluate your responses:

Mechanics Problems (1-3)

  • Correctly identified relevant equations
  • Proper substitution of values with units
  • Accurate calculations
  • Final answer with correct units

Energy Problems (4-5)

  • Applied conservation of energy correctly
  • Identified energy transformations
  • Used correct formulas for KE, PE, and work

Investigation Skills (6-7)

  • Calculated mean, range, and uncertainty correctly
  • Computed percent error accurately
  • Identified reasonable sources of error

Data Analysis (8-9)

  • Calculated slope correctly
  • Found area under graph accurately
  • Identified correct linearization strategy

CER Writing (10-12)

  • Claim directly answers the question
  • Evidence includes specific numerical data
  • Reasoning connects evidence to scientific principles

Next Steps

  • Review any topics where you struggled on the checkpoint
  • Return to specific lessons for additional practice
  • Proceed to the next unit when you feel confident
  • Use this physics foundation for SAT/ACT science reasoning practice