Q: A car starts from rest and accelerates uniformly at $$2\ \mathrm{m/s^2$}$$ for $$5\ \mathrm{s}. $$What is its final velocity?

$$v = 2 \times 5 = 10\ \mathrm{m/s}$$

Q: Which of the following is the correct formula for the dot product of two vectors $$\vec{A}$$ and $$\vec{B}$$?

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

Q: A ball is thrown straight up with an initial velocity of $$20\ \mathrm{m/s}. $$What is its velocity after $$2\ \mathrm{s}$$? (Take $$g = 9.8\ \mathrm{m/s^2$}$$ downward.)

$$v = 20 - 9.8 \times 2 = 0.4\ \mathrm{m/s}$$

Question 1

Which of the following statements best distinguishes a vector from a scalar quantity?

Accepted Answer

A vector has both magnitude and direction, while a scalar has only magnitude.

Question 2

A displacement vector has components $$b_x = 7\ \mathrm{m}$$ and $$b_y = -5\ \mathrm{m}. $$What is the magnitude of the displacement vector $$\vec{b}$$?

Accepted Answer

$$\sqrt{7^2$ + (-5)^2$} = \sqrt{74} \approx 8.6\ \mathrm{m}$$

Question 3

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

Accepted Answer

$$b_x = b \cos 	heta$$

Question 4

If two vectors $$\vec{a}$$ and $$\vec{b}$$ are added, which property ensures that $$\vec{a} + \vec{b} = \vec{b} + \vec{a}$$?

Accepted Answer

Commutative property

Question 5

A car starts from rest and accelerates uniformly at $$2\ \mathrm{m/s^2$}$$ for $$5\ \mathrm{s}. $$What is its final velocity?

Accepted Answer

$$v = 2 	imes 5 = 10\ \mathrm{m/s}$$

Question 6

Which of the following is the correct formula for the dot product of two vectors $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

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

Question 7

A ball is thrown straight up with an initial velocity of $$20\ \mathrm{m/s}. $$What is its velocity after $$2\ \mathrm{s}$$? (Take $$g = 9.8\ \mathrm{m/s^2$}$$ downward.)

Accepted Answer

$$v = 20 - 9.8 	imes 2 = 0.4\ \mathrm{m/s}$$

Question 8

Which of the following best describes the direction of the vector resulting from the cross product $$\vec{A} 	imes \vec{B}$$?

Accepted Answer

Perpendicular to the plane containing $$\vec{A}$$ and $$\vec{B}$$

Question 9

A cyclist moves from position $$x_1 = -3$$\ \mathrm{m}$$ to x_2$ = -7\ \mathrm{m}. $$What is the displacement?

Accepted Answer

$$\Delta x = -7 - (-3) = -4\ \mathrm{m}$$

Question 10

Which of the following is true about the magnitude of a vector under a rotation of the coordinate system?

Accepted Answer

The magnitude remains the same.

Question 11

A car with an initial velocity of $$-25\ \mathrm{m/s} is $$brought to rest in $$5.0\ \mathrm{s}. $$What is its acceleration?

Accepted Answer

$$a = \frac{0 - (-25)}{5} = 5\ \mathrm{m/s^2$}$$

Question 12

Which of the following is the correct formula for the position $$x of an $$object under constant acceleration $$a$$ after time $$t$$, starting from initial position $$x_0$$ and initial velocity $$v_0$$?

Accepted Answer

$$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$

Question 13

If the dot product of two vectors $$\vec{A}$$ and $$\vec{B} is $$zero, what can be concluded about the angle $$	heta$$ between them?

Accepted Answer

$$	heta = 90^\circ$$

Question 14

A vector $$\vec{v} is $$multiplied by a negative scalar $$c. $$What happens to the direction of the resulting vector?

Accepted Answer

It reverses direction.

Question 15

Which of the following is NOT a valid vector operation?

Accepted Answer

Adding a displacement vector and a velocity vector

Question 16

A ball is thrown upward. At the highest point of its trajectory, what is the acceleration of the ball?

Accepted Answer

$$a = -9.8\ \mathrm{m/s^2$}$$ downward

Question 17

If $$\vec{A} = 3\hat{i} + 4\hat{j}$$, what is the angle $$	heta$$ between $$\vec{A}$$ and the positive $$x-$$axis?

Accepted Answer

$$	heta = \arctan\left(\frac{4}{3}ight)$$

Vectors and Kinematics: Foundations for Physics with Calculus

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