Q1. What is 3.891 µm expressed in proper scientific notation?

Background

Topic: Scientific Notation and Unit Conversion

This question tests your ability to convert between metric prefixes and express quantities in scientific notation, which is essential for clear communication in physics.

Key Terms and Formulas:

• 1 micrometer (µm) = meters (m)

• Scientific notation: , where and is an integer.

Step-by-Step Guidance

1. Recognize that the prefix "micro" (µ) means , so meters.

2. Check if the number is already in proper scientific notation (i.e., a number between 1 and 10 multiplied by a power of 10).

3. Compare this result to the answer choices to see which matches the correct scientific notation.

Try solving on your own before revealing the answer!

Q2. A long-distance runner runs 32 complete laps around a 400-m track in 72 min. Which of the following statements is true?

Background

Topic: Displacement vs. Distance

This question tests your understanding of the difference between displacement (a vector) and distance (a scalar), as well as concepts of average velocity and position.

Key Terms and Formulas:

• Distance: Total length of the path traveled (scalar).

• Displacement: Change in position from start to finish (vector).

• Average velocity:

Step-by-Step Guidance

1. Calculate the total distance: $32\times m per lap.

2. Think about the runner's starting and ending positions after 32 complete laps on a closed track.

3. Recall that displacement depends only on the initial and final positions, not the path taken.

4. Review each statement in the answer choices and use your understanding of distance and displacement to evaluate their correctness.

Try solving on your own before revealing the answer!

Q3. Which of the following is a scalar quantity?

Background

Topic: Scalars vs. Vectors

This question tests your ability to distinguish between scalar and vector quantities in physics.

Key Terms and Formulas:

• Scalar: A quantity with magnitude only (no direction).

• Vector: A quantity with both magnitude and direction.

Step-by-Step Guidance

1. Review the definitions of scalar and vector quantities.

2. Go through each answer choice and determine whether it has direction associated with it.

3. Recall that quantities like velocity, acceleration, and displacement are vectors, while time is a scalar.

Try solving on your own before revealing the answer!

Q4. Which of the following statements about projectile motion in the absence of air resistance is true?

Background

Topic: Projectile Motion

This question tests your understanding of the kinematics of projectile motion, especially the behavior of velocity and acceleration components.

Key Terms and Formulas:

• Horizontal acceleration (): $0$ (no air resistance)

• Vertical acceleration (): (downward, due to gravity)

• Initial and final velocities in and directions

Step-by-Step Guidance

1. Recall that in projectile motion without air resistance, the only acceleration is due to gravity and acts vertically downward.

2. Consider the horizontal () and vertical () components of velocity and acceleration.

3. Review each statement and use your knowledge of projectile motion to determine which is correct.

Try solving on your own before revealing the answer!

Q5. One lightyear is a measure of distance equal to meters, the distance light travels in one year. How many lightyears are in 3.000 nm?

Background

Topic: Unit Conversion and Scientific Notation

This question tests your ability to convert between different units of length, especially using scientific notation and metric prefixes.

Key Terms and Formulas:

• 1 nanometer (nm) = meters

• 1 lightyear = meters

• To convert:

Step-by-Step Guidance

1. Convert 3.000 nm to meters using the metric prefix.

2. Set up the ratio to convert meters to lightyears using the given value for one lightyear.

3. Write the expression in scientific notation and simplify the powers of ten.

Try solving on your own before revealing the answer!

Q6. You are biking home from a football game. You start biking at 6.4 m/s for 5 min; it then starts raining and you instantaneously slow down. It takes you 23 minutes of biking in the rain to get home. Your route home is a total of 6.2 km. With what speed in m/s did you bike in the rain?

Background

Topic: Average Speed and Kinematics

This question tests your ability to use the relationship between distance, speed, and time, and to solve for an unknown speed when given total distance and time intervals at different speeds.

Key Terms and Formulas:

• Distance = speed × time:

• Total distance = distance at first speed + distance at second speed

• Convert all times to seconds or all distances to meters for consistency.

Step-by-Step Guidance

1. Convert all times to seconds and the total distance to meters.

2. Calculate the distance covered at the initial speed using .

3. Subtract this distance from the total distance to find the distance covered in the rain.

4. Set up the equation to solve for the speed in the rain, .

Try solving on your own before revealing the answer!

Q7. You drop a stone from a bridge that is 13 m above the water. How long in seconds does it take the stone to reach the water?

Background

Topic: Free Fall Kinematics

This question tests your ability to use kinematic equations for objects in free fall under gravity.

Key Terms and Formulas:

• Displacement:

• For free fall: , (downward)

• Distance fallen:

Step-by-Step Guidance

1. Set up the equation for vertical displacement: .

2. Plug in m and m/s².

3. Rearrange the equation to solve for .

Try solving on your own before revealing the answer!

Q8. A pitcher throws a baseball horizontally at 42 m/s. A catcher catches the ball just as it hits the ground 18.4 m away. How far in meters did the ball drop from the release point to the ground?

Background

Topic: Projectile Motion (Horizontal Launch)

This question tests your ability to analyze projectile motion, specifically the vertical displacement when an object is launched horizontally.

Key Terms and Formulas:

• Horizontal motion:

• Vertical motion:

• Initial vertical velocity is zero for horizontal launch.

Step-by-Step Guidance

1. Calculate the time it takes for the ball to travel 18.4 m horizontally using .

2. Use this time in the vertical motion equation to find the vertical drop: .

3. Plug in the values for and to set up the calculation for the vertical distance.

Try solving on your own before revealing the answer!

Q9. In the equation , x has units of meters and t has units of seconds. What are the units of b?

Background

Topic: Dimensional Analysis

This question tests your ability to use dimensional analysis to determine the units of a constant in an equation.

Key Terms and Formulas:

• Dimensional analysis: Equate the units on both sides of the equation.

• Units of : meters (m)

• Units of : seconds (s)

Step-by-Step Guidance

1. Write the units for each term in the equation: .

2. Since is in meters, each term on the right must also have units of meters.

3. Set up the units for and solve for the units of .

Try solving on your own before revealing the answer!

Q10. Your friend pitches a ball horizontally at 6.6 m/s. If your friend instead throws the ball straight up and then catches it, how much time in seconds passes between the toss and the catch, assuming they occur at the same height?

Background

Topic: Vertical Projectile Motion (Symmetric Flight)

This question tests your understanding of the time of flight for an object thrown vertically upward and returning to the same height.

Key Terms and Formulas:

• Time to reach maximum height:

• Total time:

• m/s²

Step-by-Step Guidance

1. Use the formula for time to reach the top: , where is the initial vertical velocity.

2. Double this time to get the total time for the ball to go up and come back down to the same height.

3. Plug in the given value for and to set up the calculation.

Try solving on your own before revealing the answer!

Q11. You bike to The Swamp by traveling 2.0 mi in a direction 20° N of E, and then you travel 0.50 mi in a direction 15° W of N. What is the distance in miles a bird would fly from your starting point straight to your ending point?

Background

Topic: Vector Addition and Resultant Displacement

This question tests your ability to add vectors using components and find the magnitude of the resultant vector.

Key Terms and Formulas:

• Vector components: ,

• Resultant vector:

Step-by-Step Guidance

1. Break each leg of the trip into and components using the given angles.

2. Add the and components separately to get the total displacement vector.

3. Use the Pythagorean theorem to find the magnitude of the resultant vector (straight-line distance).

Try solving on your own before revealing the answer!

Q12. The acceleration due to gravity on the moon is 1.6 m/s². You kick a soccer ball on the moon at 5.3 m/s angled 12° above the horizontal. If it lands 7.1 m away, what is the maximum height it reached in meters?

Background

Topic: Projectile Motion (Non-Earth Gravity)

This question tests your ability to analyze projectile motion with a given initial velocity, angle, and different gravitational acceleration.

Key Terms and Formulas:

• Initial velocity components: ,

• Range: (for symmetric flight)

• Maximum height:

Step-by-Step Guidance

1. Calculate the initial velocity components using the given angle.

2. Use the range formula or kinematic equations to check consistency with the given range.

3. Use the vertical component to set up the formula for maximum height: .

Try solving on your own before revealing the answer!