Q: Which of the following is true about the cross product (vector product) of two vectors $$\vec{A}$$ and $$\vec{B}$$?

$$\vec{A} \times \vec{B} is $$perpendicular to both $$\vec{A}$$ and $$\vec{B}$$

Question 1

Which of the following is NOT a fundamental quantity in the International System (SI) of units?

Accepted Answer

Temperature

Question 2

A train accident occurred due to a small percent error in a measurement. Which concept does this best illustrate?

Accepted Answer

The necessity of significant figures and uncertainty analysis

Question 3

A vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$5$$

Question 4

Which of the following best describes the result of multiplying a vector $$\vec{A} by a $$negative scalar $$-3$$?

Accepted Answer

A vector three times as long as $$\vec{A}$$, pointing in the opposite direction

Question 5

A projectile is launched horizontally from a cliff. Neglecting air resistance, which statement is true about its motion?

Accepted Answer

The horizontal velocity remains constant while the vertical velocity increases linearly with time

Question 6

Given vectors $$\vec{A}$$ and $$\vec{B}$$, the scalar (dot) product is defined as:

Accepted Answer

$$\vec{A} \cdot \vec{B} = AB \cos \phi$$

Question 7

A car moves along a straight road. Its position as a function of time is given by $$x(t) = 4t^2$ + 2t + 1. $$What is the instantaneous velocity at $$t = 3 s$$?

Accepted Answer

$$v = 26 m/s$$

Question 8

Which of the following is true about the cross product (vector product) of two vectors $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

$$\vec{A} 	imes \vec{B} is $$perpendicular to both $$\vec{A}$$ and $$\vec{B}$$

Question 9

A runner completes a 400 m lap in 50 s. What is the magnitude of the average velocity if the runner finishes at the starting point?

Accepted Answer

$$0 m/s$$

Question 10

A ball is thrown straight up with an initial velocity of $$15 m/s. $$What is its velocity at the highest point?

Accepted Answer

$$0 m/s$

Question 11

Which of the following is a correct statement about the addition of vectors?

Accepted Answer

The sum of vectors is independent of the order in which they are added

Question 12

A car accelerates from rest at a constant acceleration of $$2 m/s$^2. $$How far does it travel in $$5$$ seconds?

Accepted Answer

$$25 m$$

Question 13

Which of the following is the correct expression for the $$x-$$component of a vector $$\vec{A}$$ with magnitude $$A$$ and angle $$	heta$$ from the $$x-$$axis?

Accepted Answer

$$A_x = A \cos 	heta$$

Question 14

A vector $$\vec{A}$$ has components $$A_x = -3$$ and $$A_y = 4. $$What is the direction angle $$	heta ($$measured counterclockwise from the $$x-$$axis)?

Accepted Answer

$$126.9^\circ$$

Question 15

A cyclist rides 2 km east, then 1 km north. What is the magnitude of the resultant displacement?

Accepted Answer

$$\sqrt{5} km$$

Question 16

Which of the following is the correct formula for the relative velocity of object P with respect to frame A, given its velocity relative to frame B and the velocity of frame B relative to frame A?

Accepted Answer

$$v_{P/A} = v_{P/B} + v_{B/A}$$

Question 17

A ball is thrown horizontally from a height of $$20 m $$with a speed of $$10 m/s. $$Neglecting air resistance, how long does it take to hit the ground?

Accepted Answer

$$2.02 s$$

Question 18

Which of the following statements about unit vectors is correct?

Accepted Answer

Unit vectors have a magnitude of 1 and no units

Question 19

If $$\vec{A} = 2\hat{i} + 3\hat{j}$$ and $$\vec{B} = -\hat{i} + 4\hat{j}$$, what is $$\vec{A} \cdot \vec{B}$$?

Accepted Answer

$$8$$

Question 20

A car moves in a circle of radius $$10 m at a $$constant speed of $$5 m/s. $$What is the magnitude of its centripetal acceleration?

Accepted Answer

$$0.5 m/s$^2$$

Physics with Calculus: Units, Physical Quantities, and Vectors (Chapters 1–3 Study Guide)

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