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Quiz: Vector Math Fundamentals & Physics Acceleration

Test your understanding of p5.Vector, magnitude, normalization, dot product, and Newton's laws of motion with these review questions.

1. What two fundamental physical quantities are encapsulated in a Euclidean vector?

  1. Magnitude (length) and Direction
  2. Color and Transparency
  3. Mass and Temperature
  4. Frequency and Wavelength
Show Answer

The correct answer is A. A vector in 2D or 3D space represents an entity having both a magnitude (length or speed) and a directional orientation. Options A, C, and D are scalar or non-geometric properties.

Concept Tested: Vector Definition

2. Which p5.js function instantiates a new 2D or 3D vector object?

  1. createVector(x, y, [z])
  2. newVector(x, y)
  3. makeVector(x, y)
  4. vector(x, y)
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The correct answer is A. createVector(x, y, [z]) creates a new instance of the p5.Vector class. Options B, C, and D are not standard p5.js factory functions.

Concept Tested: Create Vector Function

3. According to Newton's Second Law of Motion ($F = m \cdot a$), how is acceleration calculated from applied force and mass?

  1. acceleration = force * mass
  2. acceleration = force / mass
  3. acceleration = mass / force
  4. acceleration = force + mass
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The correct answer is B. Rearranging $F = m \cdot a$ yields $a = F / m$. Acceleration is directly proportional to net force and inversely proportional to mass. Options A, C, and D are algebraic errors.

Concept Tested: Newton Second Law Integration

4. What is the magnitude of a unit vector obtained by calling v.normalize()?

  1. 0
  2. 1
  3. TWO_PI
  4. Equal to the canvas diagonal
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The correct answer is B. Normalizing a vector scales its components so that its length (magnitude) becomes exactly 1 unit while preserving its original direction. Options A, C, and D are incorrect.

Concept Tested: Vector Normalization Unit

5. Given two vectors pos and vel, how do you update position by adding velocity in place using p5.Vector methods?

  1. pos = add(pos, vel);
  2. pos.add(vel);
  3. pos += vel;
  4. pos.append(vel);
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The correct answer is B. p5.Vector.prototype.add() adds the components of the passed vector to the calling vector in place. Option C (pos += vel) fails in JavaScript because + does not support vector operator overloading.

Concept Tested: Vector Addition Add

6. What does the dot product v1.dot(v2) return if two vectors are perpendicular (orthogonal) to each other?

  1. 1
  2. -1
  3. 0
  4. Infinity
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The correct answer is C. The dot product is defined as $|v1| \cdot |v2| \cdot \cos(\theta)$. When two vectors are perpendicular, $\theta = 90^\circ$ and $\cos(90^\circ) = 0$, yielding a dot product of 0. Options A, C, and D are incorrect.

Concept Tested: Vector Dot Product Orthogonal

7. To limit a particle's maximum speed to 10, which p5.Vector method should be called on its velocity vector?

  1. vel.max(10);
  2. vel.constrain(10);
  3. vel.limit(10);
  4. vel.cap(10);
Show Answer

The correct answer is C. vel.limit(max) caps the magnitude of the vector at max without altering its direction if it exceeds max. Options B, C, and D are not p5.Vector methods.

Concept Tested: Vector Limit Speed

8. Why must acceleration be reset to zero (acc.mult(0)) at the end of each frame's physics update in Euler integration?

  1. To reset the particle back to origin (0, 0)
  2. To stop the particle from moving
  3. To clear accumulated forces so forces do not persist and multiply indefinitely across subsequent frames
  4. To save memory in the garbage collector
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The correct answer is C. Forces act instantaneously or continuously per frame. If acceleration is not cleared to zero (acc.set(0, 0)), forces from previous frames accumulate indefinitely, causing runaway exponential acceleration. Options B, C, and D are false.

Concept Tested: Accumulate Forces Newton

9. How do you calculate a vector pointing from particle A to target B?

  1. let dir = p5.Vector.dist(targetB, posA);
  2. let dir = p5.Vector.add(targetB, posA);
  3. let dir = p5.Vector.mult(targetB, posA);
  4. let dir = p5.Vector.sub(targetB, posA);
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The correct answer is D. Subtracting the starting position vector from the target position vector (target - current) yields the vector pointing from posA to targetB. Option B sums them. Option D returns a scalar distance, not a vector.

Concept Tested: Vector Subtraction Direction

10. What is the visual difference between updating motion with velocity alone versus velocity plus acceleration?

  1. Acceleration locks frameRate to 30 FPS
  2. Acceleration only works in 3D WebGL
  3. Velocity alone moves randomly
  4. Velocity alone produces constant speed linear motion, while acceleration produces curved trajectories, gravity arcs, and steering behaviors
Show Answer

The correct answer is D. Position updated only by constant velocity yields fixed-speed straight lines. Acceleration continuously alters velocity's speed and direction, enabling gravity curves, drag deceleration, and realistic physics. Options B, C, and D are false.

Concept Tested: Velocity vs Acceleration Motion