11.1.A.1–2Multiple Choice
Which statement correctly distinguishes a scalar from a vector?
Select A, B, C, or D to check your answer.
Directions: Work each problem on your own paper first. For multiple choice, select A, B, C, or D. You will see right away whether you are correct. If you miss, you will see the most likely reason, and you can try again. For short response, type your answer, then compare it with the model solution. Questions mix the five essential knowledge threads of Topic 1.1 — the scalar/vector distinction and the arrow model, classifying physical quantities as scalars or vectors, unit vector notation versus magnitude-and-direction form, position vectors and resultants, and the sign convention used in one-dimensional problems. Round decimals to the nearest tenth unless noted otherwise.
Which statement correctly distinguishes a scalar from a vector?
Select A, B, C, or D to check your answer.
A weather report says the temperature is 72°F and the wind is blowing at 15 mph from the west. (a) Identify which of these two quantities is a scalar and which is a vector. (b) Explain your reasoning for each.
Two arrows are drawn representing two different vectors. Arrow 1 is twice as long as Arrow 2, and both point in the same direction. Which statement is correct?
Select A, B, C, or D to check your answer.
A vector is drawn as an arrow 3 cm long, pointing due north, using a scale of 1 cm = 5 m. (a) Find the magnitude of the vector it represents. (b) If a second vector of magnitude 35 m, also pointing due north, were drawn using the same scale, how long would its arrow be? (c) Explain why these two arrows would have different lengths despite pointing in the same direction.
Which of the following is a vector quantity?
Select A, B, C, or D to check your answer.
A delivery truck drives 12 km east, then 5 km west, to make two stops. (a) Find the total distance traveled. (b) Find the displacement from start to end. (c) Classify each result as a scalar or a vector.
A cyclist's position changes from being 3 km east of a landmark to being 1 km west of that same landmark. Which of the following quantities would NOT require a direction to be fully specified?
Select A, B, C, or D to check your answer.
Using the definitions of distance, speed, position, displacement, velocity, and acceleration, explain why physicists find it useful to split quantities into scalars and vectors rather than treating every physical quantity the same way.
A vector is given as v = 9î + 12ĵ (m/s). What is its magnitude?
Select A, B, C, or D to check your answer.
A vector has magnitude 20 N, directed 60° above the +x axis. (a) Find its x-component. (b) Find its y-component. (c) Write the vector in unit vector notation.
A vector is given as A = 5î − 12ĵ (meters). What angle does this vector make with the +x axis (reported as a positive value, measured below the axis since the y-component is negative)?
Select A, B, C, or D to check your answer.
A vector is given in three dimensions as r = 1î + 2ĵ + 2k̂ (meters). (a) Find its magnitude. (b) Explain why the Pythagorean theorem can be extended to three dimensions, and state the general formula you used.
A particle's position vector is r = 6î + 8ĵ (meters). What is the unit vector r̂ in the direction of r?
Select A, B, C, or D to check your answer.
Vector A = −2î + 7ĵ and vector B = 6î − 3ĵ (meters). (a) Find the resultant R = A + B. (b) Find |R|.
A particle starts at position r₀ = 2î − 1ĵ (m) and undergoes a displacement of d = 3î + 5ĵ (m). What is its final position vector rf?
Select A, B, C, or D to check your answer.
Four forces act on an object: F₁ = 3î, F₂ = −1î + 4ĵ, F₃ = 2ĵ, and F₄ = −2î − 1ĵ (all in newtons). (a) Find the resultant force (the sum of all four). (b) Find the magnitude of this resultant.
On a number line where rightward is positive, a particle's velocity is −8 m/s. In which direction is the particle moving?
Select A, B, C, or D to check your answer.
A particle moves from x₀ = 10 m to xf = −4 m along a 1D axis where rightward is positive. (a) Find the particle's displacement, including its sign. (b) State which direction the particle moved. (c) If the positive direction had instead been defined as leftward, what would the displacement's sign be, and would the particle's actual motion have changed?
Which statement about signs and direction in a one-dimensional coordinate system is correct?
Select A, B, C, or D to check your answer.
A ball is thrown straight up and caught at the same height. Taking upward as positive, its velocity is +15 m/s the instant it leaves the thrower's hand and −15 m/s the instant it's caught. (a) Explain what the sign change tells you about the ball's motion. (b) Find the ball's average velocity for the entire up-and-down trip, and explain whether the sign convention affects this result. (c) Contrast average velocity with average speed for this same trip.