Q1. Which of the following is the dimensional formula for velocity?

Background

Topic: Dimensional Analysis

This question tests your understanding of how physical quantities are represented in terms of fundamental dimensions (length, mass, time, etc.). Velocity is a basic kinematic quantity.

Key Terms and Formulas:

• Velocity: The rate of change of displacement with respect to time.

• Dimensional formula: Expresses a physical quantity in terms of the basic dimensions (L for length, M for mass, T for time).

For velocity:

Displacement has dimension , time has dimension .

Step-by-Step Guidance

1. Recall that velocity is displacement divided by time.

2. Write the dimensional formula for displacement () and time ().

3. Set up the dimensional formula for velocity as .

4. Compare this with the options given to identify the correct one.

Try solving on your own before revealing the answer!

Q2. An object's velocity-time graph shows a flat, horizontal line (not at zero) between s and s. Which of the following is true about the object during this time interval?

Background

Topic: Kinematics – Interpreting Graphs

This question tests your ability to interpret velocity-time graphs and understand what a constant velocity means for acceleration and motion.

Key Terms and Concepts:

• Velocity-time graph: Shows how velocity changes with time.

• Flat, horizontal line: Indicates constant velocity.

• Acceleration: The rate of change of velocity with respect to time.

Step-by-Step Guidance

1. Recall that a flat, horizontal line on a velocity-time graph means the velocity is constant.

2. Think about what constant velocity implies for acceleration (is velocity changing?).

3. Review the options and identify which one matches the physical meaning of constant velocity.

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Q3. A remote-control car has a velocity vector m/s. What is the magnitude of the car's speed?

Background

Topic: Vectors – Magnitude of a Vector

This question tests your ability to calculate the magnitude of a two-dimensional velocity vector.

Key Terms and Formulas:

• Vector components: m/s, m/s

• Magnitude of a vector:

Step-by-Step Guidance

1. Identify the x and y components of the velocity vector.

2. Recall the formula for the magnitude of a vector in two dimensions.

3. Plug in the values for and into the formula .

4. Set up the calculation, but do not compute the final value yet.

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Q4. A heavy box is being pushed across a horizontal floor at a constant speed in a straight line. Which statement about the forces acting on the box is true?

Background

Topic: Newton's Laws – Force Equilibrium

This question tests your understanding of Newton's First Law and the concept of net force when an object moves at constant velocity.

Key Terms and Concepts:

• Constant speed: Implies zero acceleration.

• Net force: The vector sum of all forces acting on an object.

• Equilibrium: When net force is zero.

Step-by-Step Guidance

1. Recall Newton's First Law: An object in motion at constant velocity has zero net force acting on it.

2. Consider the forces acting: pushing force, friction, normal force, and weight.

3. Think about what must be true about the net force if the box moves at constant speed.

4. Review the answer choices and match them to the physical situation.

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Q5. A baseball is thrown straight upward. At the very peak of its flight, which of the following is true?

Background

Topic: Kinematics – Free Fall

This question tests your understanding of the motion of objects under gravity, especially at the highest point of their trajectory.

Key Terms and Concepts:

• At the peak: The instant when the object changes direction from upward to downward.

• Velocity at the peak: Zero (momentarily).

• Acceleration due to gravity: Always acts downward, m/s.

Step-by-Step Guidance

1. Recall what happens to the velocity of an object at the peak of its upward motion.

2. Remember that gravity acts on the object throughout its flight, including at the peak.

3. Identify the correct combination of velocity and acceleration at the peak.

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Q6. Write to 3 significant figures.

Background

Topic: Significant Figures and Scientific Notation

This question tests your ability to express numbers in scientific notation with the correct number of significant digits.

Key Terms and Concepts:

• Significant figures: The digits in a number that carry meaning contributing to its precision.

• Scientific notation: Expressing numbers as where .

Step-by-Step Guidance

1. Identify how many significant figures are in the original number.

2. Express the number in the form with three significant digits.

3. Adjust the coefficient so that it has three digits (including zeros if necessary).

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Q7. A hiker walks in two stages. Their displacement vectors are m and m. (a) Determine the resultant displacement vector . (b) Determine the vector difference . (c) Determine the scalar (dot) product . (d) Determine the angle of the resultant displacement vector relative to the positive x-axis.

Background

Topic: Vectors – Addition, Subtraction, Dot Product, and Angles

This problem tests your ability to perform vector operations in two dimensions, including addition, subtraction, dot product, and finding the angle of a vector.

Key Terms and Formulas:

• Vector addition:

• Vector subtraction:

• Dot product:

• Angle with x-axis:

Step-by-Step Guidance

1. For (a), add the corresponding components of and to find .

2. For (b), subtract the components of from to find the difference vector.

3. For (c), use the dot product formula with the given components.

4. For (d), use the components of to set up the formula for the angle with respect to the x-axis.

5. Write out the expressions for each part, but do not compute the final values yet.

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Q8. A stunt driver drives a car horizontally off a 20 m high cliff at a speed of 15 m/s. Air resistance is neglected. ( m/s) (a) How long is the car in the air before it hits the ground below? (b) How far horizontally from the base of the cliff does the car land? (c) What is the vertical component of the car's velocity just before it hits the ground? (d) What is the magnitude of the car's total velocity just before impact?

Background

Topic: Projectile Motion

This problem tests your understanding of two-dimensional kinematics, specifically horizontal projectile motion.

Key Terms and Formulas:

• Vertical motion:

• Horizontal motion:

• Vertical velocity at impact:

• Total velocity magnitude:

Step-by-Step Guidance

1. For (a), set up the vertical motion equation with m, , and .

2. Solve for the time it takes to fall 20 m.

3. For (b), use the time from (a) and the horizontal velocity to set up the equation for horizontal distance.

4. For (c), use the time from (a) to set up the equation for the vertical velocity just before impact.

5. For (d), set up the equation for the magnitude of the total velocity using the horizontal and vertical components.

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Q9. A car traveling horizontally at 25 m/s suddenly slams on the brakes. It comes to a complete stop in 3.5 s with constant deceleration. (a) What is the magnitude of the car's acceleration? (b) How far does the car travel while it is braking?

Background

Topic: Kinematics – Uniform Acceleration

This problem tests your ability to use kinematic equations to solve for acceleration and displacement during constant acceleration (deceleration).

Key Terms and Formulas:

• Initial velocity: m/s

• Final velocity: m/s

• Time: s

• Acceleration:

• Displacement:

Step-by-Step Guidance

1. For (a), use the acceleration formula with the given initial and final velocities and time.

2. Set up the calculation for acceleration, but do not compute the final value yet.

3. For (b), use the displacement formula with the known values and the acceleration from (a).

4. Set up the calculation for displacement, but do not compute the final value yet.

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Q10. A 40 kg box is on a frictionless horizontal floor. A person pulls on the box with a force of 150 N at an angle of 30 above the horizontal. ( m/s) (a) Draw the free body diagram of the box. (b) What is the horizontal acceleration of the box? (c) What is the Normal force acting on the box from the floor?

Background

Topic: Newton's Second Law – Forces and Free Body Diagrams

This problem tests your ability to resolve forces into components, apply Newton's Second Law, and analyze vertical and horizontal forces.

Key Terms and Formulas:

• Force components: ,

• Newton's Second Law:

• Normal force: Balances the vertical forces (weight and vertical component of pull)

Step-by-Step Guidance

1. For (a), sketch the box and draw all forces: weight (down), normal force (up), pulling force (at 30 above horizontal).

2. For (b), resolve the pulling force into horizontal and vertical components.

3. Set up Newton's Second Law in the horizontal direction to solve for acceleration.

4. For (c), set up the vertical force balance equation to solve for the normal force.

5. Write out the expressions for acceleration and normal force, but do not compute the final values yet.

Try solving on your own before revealing the answer!

Q11. Suppose you launch a ball from a height of 4 m with an initial velocity of 5 m/s making a 0 angle with the horizontal. (a) How much time does it take to reach the floor? (b) How far horizontally does the ball reach on the floor?

Background

Topic: Projectile Motion – Horizontal Launch

This problem tests your ability to analyze projectile motion when the initial vertical velocity is zero and the object is launched horizontally from a height.

Key Terms and Formulas:

• Vertical motion:

• Horizontal motion:

Step-by-Step Guidance

1. For (a), set up the vertical motion equation with m, , and .

2. Solve for the time it takes to fall 4 m.

3. For (b), use the time from (a) and the horizontal velocity to set up the equation for horizontal distance.

4. Write out the expressions, but do not compute the final values yet.

Try solving on your own before revealing the answer!

Q12. A child of mass 20 kg rides on a toboggan down a slick, ice-covered hill inclined at an angle of 30 with respect to the horizontal. (a) Draw the Free body diagram of the child. (b) What is the acceleration of the child? (c) What is the normal force exerted on the child by the toboggan?

Background

Topic: Newton's Second Law – Inclined Planes

This problem tests your ability to resolve forces on an inclined plane and apply Newton's Second Law to find acceleration and normal force.

Key Terms and Formulas:

• Weight:

• Component of gravity down the incline:

• Normal force:

• Acceleration:

Step-by-Step Guidance

1. For (a), sketch the child on the incline and draw all forces: weight (down), normal force (perpendicular to incline), and friction (if any; here, it's frictionless).

2. For (b), resolve the weight into components parallel and perpendicular to the incline.

3. Set up Newton's Second Law along the incline to solve for acceleration.

4. For (c), set up the equation for the normal force using the perpendicular component of weight.

5. Write out the expressions for acceleration and normal force, but do not compute the final values yet.

Try solving on your own before revealing the answer!