Q1. What is the approximate distance between the Earth and the Moon?

Background

Topic: Units and Orders of Magnitude

This question tests your understanding of astronomical distances and your ability to estimate and compare large-scale measurements using scientific notation.

Key Terms:

• Distance: The length between two points, often measured in kilometers (km) for astronomical objects.

• Scientific notation: A way to express very large or very small numbers using powers of ten.

Step-by-Step Guidance

1. Recall that the Earth-Moon distance is a commonly cited value in physics and astronomy. Think about the scale: is it closer to hundreds, thousands, or hundreds of thousands of kilometers?

2. Compare the answer choices. Notice the difference in orders of magnitude (e.g., 380 km vs. 380,000 km).

3. Use scientific notation to help visualize the size of each option. For example, .

4. Consider what you know about the Moon's orbit and typical values for planetary distances.

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Q2. What is the number of seconds in one year?

Background

Topic: Unit Conversion

This question tests your ability to convert units, specifically from years to seconds, using multiplication and knowledge of time units.

Key Terms and Formulas:

• Unit conversion: Changing from one unit to another using conversion factors.

• Time units: 1 year = 365 days (or 365.25 for leap years), 1 day = 24 hours, 1 hour = 60 minutes, 1 minute = 60 seconds.

Step-by-Step Guidance

1. Start by writing the conversion factors: , , , .

2. Set up the multiplication: .

3. Multiply the numbers step by step, keeping track of units at each stage.

4. Check if the answer choices match your calculated value, paying attention to scientific notation and significant digits.

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Q3. How many protons (mp = 1.67 x 10-27 kg) are there in a 70.0 kg person? Assume they are completely made of protons.

Background

Topic: Scientific Notation and Mass Calculation

This question tests your ability to use scientific notation and perform calculations involving mass and the number of particles.

Key Terms and Formulas:

• Proton mass:

• Number of protons:

• Scientific notation: Expressing numbers as

Step-by-Step Guidance

1. Write the formula for the number of protons:

2. Set up the division, noting that the units (kg) will cancel out, leaving a pure number.

3. Divide 70.0 by 1.67 to get the coefficient.

4. Apply the exponent rules for scientific notation: .

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Q4. In the expression , m has units of mass, and k has units of mass divided by time squared. What are the units of T?

Background

Topic: Dimensional Analysis

This question tests your ability to analyze the units in a physical equation and determine the resulting units for a variable.

Key Terms and Formulas:

• Dimensional analysis: The process of determining the units of a quantity based on the units of other quantities in an equation.

• Square root:

Step-by-Step Guidance

1. Write the units for (mass, ) and (mass divided by time squared, ).

2. Set up the ratio:

3. Simplify the units:

4. Take the square root:

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Q5. Jarmilla gets her morning coffee by walking to the bodega and back. Which statement about her entire trip is true?

Background

Topic: Linear Motion, Displacement, and Velocity

This question tests your understanding of the difference between speed, velocity, and displacement in one-dimensional motion.

Key Terms:

• Displacement: The change in position from start to finish.

• Average velocity: Displacement divided by total time.

• Average speed: Total distance traveled divided by total time.

Step-by-Step Guidance

1. Consider the scenario: Jarmilla walks to the bodega and returns to her starting point.

2. Calculate her displacement: Since she ends where she started, displacement is zero.

3. Calculate her average velocity: Since displacement is zero, average velocity is also zero.

4. Think about her average speed: She traveled a nonzero distance, so average speed is not zero.

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Q6. Which scenario describes a trip with zero average velocity?

Background

Topic: Linear Motion and Average Velocity

This question tests your understanding of average velocity and how it relates to displacement.

Key Terms:

• Average velocity:

• Displacement: The net change in position.

Step-by-Step Guidance

1. Recall that zero average velocity means zero displacement over the trip.

2. Analyze each scenario: Which involves returning to the starting point?

3. Consider the dog fetching a stick and returning: The displacement is zero.

4. Compare with other options: Do any others involve zero displacement?

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Q7. Which statement correctly describes the motion represented on the graph of x vs. t?

Background

Topic: Linear Motion and Graph Interpretation

This question tests your ability to interpret position vs. time graphs and relate them to velocity and acceleration.

Key Terms:

• Position (): The location of an object at a given time.

• Velocity: The slope of the vs. graph.

• Magnitude of velocity: The absolute value of the slope.

Step-by-Step Guidance

1. Examine the graph: Is the slope positive, negative, or zero?

2. Positive slope means positive velocity; negative slope means negative velocity; zero slope means zero velocity.

3. Look for changes in the slope: Is it constant or changing?

4. Relate the slope to the answer choices: Which best matches the graph's behavior?

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