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

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

Question 1

A student walks 1000 feet in 5 minutes. What is their speed in SI units (m/s)?

Accepted Answer

$0.08\ \mathrm{m/s}$

Question 2

Which of the following is a correct unit conversion factor for converting inches to meters?

Accepted Answer

$1\ \mathrm{inch} = 0.0254\ \mathrm{m}$

Question 3

Given vectors $\vec{A} = (3, 5)$ and $\vec{B} = (5, -2)$, which of the following vectors has the same magnitude as $\vec{A}$ and $\vec{B}$?

Accepted Answer

$(3, -5)$

Question 4

What is the magnitude of $|\vec{A} - \vec{B}|$ if $|\vec{A}| = 5$ and $|\vec{B}| = 4$ and they are perpendicular?

Accepted Answer

$\sqrt{41}$

Question 5

Which of the following statements about unit vectors is correct?

Accepted Answer

A unit vector has a magnitude of $1$

Question 6

The dot product of two vectors $\vec{A}$ and $\vec{B}$ is zero. What does this imply about the vectors?

Accepted Answer

They are perpendicular to each other

Question 7

If $\vec{A} = (4, 0, 0)$ and $\vec{B} = (0, 3, 0)$, what is $\vec{A} 	imes \vec{B}$?

Accepted Answer

$(0, 0, 12)$

Question 8

Which equation correctly represents the average velocity $v_{avg}$ over a time interval $\Delta t$?

Accepted Answer

$v_{avg} = \frac{\Delta x}{\Delta t}$

Question 9

A car travels 100 m east, then 100 m north. What is the magnitude of its displacement?

Accepted Answer

$\sqrt{100^2 + 100^2} = 141.4\ \mathrm{m}$

Question 10

Which of the following best describes instantaneous velocity?

Accepted Answer

$v(t) = \frac{dx}{dt}$

Question 11

A ball is thrown vertically upward with initial speed $v_0 = 20\ \mathrm{m/s}$. How long does it take to reach its maximum height? (Assume $g = 10\ \mathrm{m/s^2}$)

Accepted Answer

$2\ \mathrm{s}$

Question 12

Which formula gives the position $x(t)$ of an object under constant acceleration $a$?

Accepted Answer

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

Question 13

Two cyclists start 10 km apart and ride toward each other at $5\ \mathrm{m/s}$. How long until they meet?

Accepted Answer

$1000\ \mathrm{s}$

Question 14

A fly moves back and forth between two cyclists riding toward each other at $5\ \mathrm{m/s}$, starting 10 km apart. If the fly's speed is $16\ \mathrm{m/s}$, how far does the fly travel before the cyclists meet?

Accepted Answer

$16\ \mathrm{km}$

Question 15

A skier slides down a $200\ \mathrm{m}$ slope in $5\ \mathrm{s}$ from rest. What is their acceleration?

Accepted Answer

$16\ \mathrm{m/s^2}$

Question 16

Which of the following is true about the cross product $\vec{A} 	imes \vec{B}$?

Accepted Answer

It results in a vector perpendicular to both $\vec{A}$ and $\vec{B}$

Question 17

If the velocity of an object is zero at a certain instant, what can be said about its instantaneous acceleration at that instant?

Accepted Answer

It can be nonzero

Question 18

Which graph best represents an object moving with constant positive acceleration?

Accepted Answer

A position vs. time graph that is a parabola opening upward

Question 19

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

Accepted Answer

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

Physics 1A: Foundations of Kinematics and Vectors

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