Skip to content

Quiz: Motion in One Dimension

Test your understanding of kinematics and one-dimensional motion concepts.

1. What is the key difference between distance and displacement?

  1. Distance is measured in meters while displacement is measured in kilometers
  2. Distance is a scalar quantity representing total path length, while displacement is a vector quantity representing the straight-line change in position
  3. Distance can be negative but displacement is always positive
  4. Distance and displacement are the same thing with different names
Show Answer

The correct answer is B. Distance is a scalar (magnitude only) that measures the total length of the path traveled, regardless of direction. Displacement is a vector (magnitude and direction) that represents the straight-line distance from starting to ending position. For example, walking around a 400-meter track gives you a distance of 400 m but a displacement of zero (you return to the start). Option A is incorrect—both use the same units. Option C reverses the truth—distance is never negative but displacement can be. Option D is wrong because they represent fundamentally different concepts.

Concept Tested: Distance and Displacement

See: Distance and Displacement

2. Which statement correctly describes velocity?

  1. Velocity is always positive
  2. Velocity includes both speed and direction
  3. Velocity and speed are always equal in magnitude
  4. Velocity cannot be zero unless an object has never moved
Show Answer

The correct answer is B. Velocity is a vector quantity that requires both magnitude (how fast) and direction (which way). This is the fundamental characteristic that distinguishes velocity from speed. Option A is incorrect—velocity can be positive, negative, or zero depending on the chosen coordinate system and direction of motion. Option C is wrong because average velocity magnitude can be less than average speed (consider a round trip where displacement is zero). Option D is false—velocity is zero whenever an object is at rest, regardless of its motion history.

Concept Tested: Velocity

See: Speed and Velocity

3. What does acceleration measure?

  1. How far an object moves
  2. How fast an object is moving
  3. The rate of change of velocity with respect to time
  4. The total distance covered per second
Show Answer

The correct answer is C. Acceleration is defined as the rate of change of velocity with respect to time, calculated as a = Δv/Δt. It tells us how quickly velocity is changing, measured in units of m/s². Option A describes displacement or distance. Option B describes speed or velocity magnitude. Option D describes average speed. Understanding that acceleration measures velocity change (not position or speed directly) is crucial for analyzing motion.

Concept Tested: Acceleration

See: Acceleration

4. On a position-time graph, what does the slope represent?

  1. Acceleration
  2. Displacement
  3. Velocity
  4. Distance traveled
Show Answer

The correct answer is C. The slope of a position-time graph equals velocity because slope = Δx/Δt, which is the definition of velocity. A steeper slope indicates higher speed, while a positive slope means motion in the positive direction and a negative slope means motion in the negative direction. A horizontal line (zero slope) indicates the object is at rest. Option A is incorrect—acceleration is the slope of a velocity-time graph, not a position-time graph.

Concept Tested: Position-Time Graphs

See: Position-Time Graphs

5. What does the area under a velocity-time graph represent?

  1. Acceleration
  2. Speed
  3. Displacement
  4. Position
Show Answer

The correct answer is C. The area under a velocity-time curve represents displacement during that time interval. This can be understood mathematically: area = velocity × time = (distance/time) × time = distance. For a rectangular region (constant velocity), area = base × height = Δt × v = displacement. For triangular regions (changing velocity), the geometric area still gives displacement. This is one of the most useful features of velocity-time graphs for solving kinematics problems.

Concept Tested: Velocity-Time Graphs

See: Velocity-Time Graphs

6. A car travels 3 blocks east, then 4 blocks north. What is the magnitude of the displacement?

  1. 1 block
  2. 5 blocks
  3. 7 blocks
  4. 12 blocks
Show Answer

The correct answer is B. Using the Pythagorean theorem, displacement = √(3² + 4²) = √(9 + 16) = √25 = 5 blocks. This is a classic 3-4-5 right triangle. The displacement is the straight-line distance from start to finish, not the total path length. Option C (7 blocks) would be the total distance traveled (3 + 4), not the displacement. The direction would be northeast, specifically at about 53° north of east.

Concept Tested: Displacement

See: Distance and Displacement

7. An object starts from rest and accelerates at 2 m/s² for 5 seconds. What is its final velocity?

  1. 2.5 m/s
  2. 7 m/s
  3. 10 m/s
  4. 25 m/s
Show Answer

The correct answer is C. Using the kinematic equation v = v₀ + at, where v₀ = 0 m/s (starts from rest), a = 2 m/s², and t = 5 s: v = 0 + (2)(5) = 10 m/s. The object gains 2 m/s of velocity each second, so after 5 seconds it has gained 10 m/s total. This is uniformly accelerated motion starting from rest.

Concept Tested: Uniformly Accelerated Motion

See: Uniformly Accelerated Motion

8. Which kinematic equation should you use when time is unknown and you need to find final velocity?

  1. v = v₀ + at
  2. x = x₀ + v₀t + ½at²
  3. v² = v₀² + 2a(x - x₀)
  4. x = x₀ + ½(v₀ + v)t
Show Answer

The correct answer is C. The equation v² = v₀² + 2a(x - x₀) relates velocities, acceleration, and displacement without requiring time. This makes it ideal when time is not given or not needed. It's particularly useful for problems involving braking distances or projectile range. Options A, B, and D all include time (t) as a variable, making them unsuitable when time is unknown.

Concept Tested: Kinematic Equations

See: Kinematic Equations

9. What is the acceleration due to gravity near Earth's surface (using the standard convention with positive upward)?

  1. +9.8 m/s²
  2. -9.8 m/s²
  3. +10 m/s²
  4. 0 m/s²
Show Answer

The correct answer is B. Using the standard physics convention where positive is upward and negative is downward, the acceleration due to gravity is a = -9.8 m/s². The negative sign indicates that gravity accelerates objects downward. This value is constant for all objects near Earth's surface, regardless of their mass. Note that if we chose a coordinate system with positive downward, then g would be +9.8 m/s², but the upward-positive convention is most common in physics courses.

Concept Tested: Acceleration (in context of free fall)

See: Free Fall

10. An object moving at constant velocity has what acceleration?

  1. A positive constant value
  2. A negative constant value
  3. Zero
  4. Continuously changing
Show Answer

The correct answer is C. Constant velocity means velocity is not changing, so Δv = 0. Since acceleration is defined as a = Δv/Δt, if Δv = 0, then a = 0. This is the defining characteristic of uniform motion—zero acceleration. Any non-zero acceleration would cause the velocity to change over time, contradicting the premise of constant velocity. This concept is fundamental to distinguishing between uniform motion and uniformly accelerated motion.

Concept Tested: Uniform Motion

See: Uniform Motion