Q: Convert 4.6 milliseconds (ms) to seconds (s) using metric prefixes.

$$4.6 \times 10$$^{-3}$$\ \mathrm{s}$$

Question 1

Which of the following is the correct application of the product rule for exponents when simplifying $$a^3$$ 	imes $$a^5$$?

Accepted Answer

$$a^{8}$$

Question 2

A car travels 60 km in 2 hours. What is its average speed in meters per second ($$\mathrm{m/s}$$)?

Accepted Answer

$$8.33\ \mathrm{m/s}$$

Question 3

Which of the following equations is dimensionally consistent for calculating distance $$d in $$meters, given velocity $$v in$$ $$\mathrm{m/s}$$ and time $$t in $$seconds?

Accepted Answer

$$d = v 	imes t$$

Question 4

Convert 4.6 milliseconds (ms) to seconds (s) using metric prefixes.

Accepted Answer

$$4.6 	imes 10$$^{-3}$$\ \mathrm{s}$$

Question 5

A vector $$\vec{A}$$ has components $$A_x = 8\ \mathrm{m}$$ and $$A_y = 6\ \mathrm{m}. $$What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$10\ \mathrm{m}$$

Question 6

Which of the following is the correct formula for the area under a curve $$f(x)$$ from $$x=a to$$ $$x=b$$?

Accepted Answer

$$\int_a^b f(x)\,dx$$

Question 7

A wooden cylinder has a radius of $$3.5\ \mathrm{cm}$$, height $$6\ \mathrm{cm}$$, and mass $$161\ \mathrm{g}. $$What is its density in $$\mathrm{kg/m^3$}$$? (Use $$V = \pi r^2$ h)$$

Accepted Answer

$$697\ \mathrm{kg/m^3$}$$

Question 8

Which of the following best describes a scalar quantity?

Accepted Answer

A measurement with magnitude only

Question 9

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

Accepted Answer

$$2\hat{i} + 6\hat{j}$$

Question 10

What is the dot product $$\vec{A} \cdot \vec{B} if$$ $$\vec{A} = 2\hat{i} + 3\hat{j}$$ and $$\vec{B} = \hat{i} + 2\hat{j}$$?

Accepted Answer

$$8$$

Question 11

A delivery truck travels 8 miles east, 5 miles north, and 4 miles east again. What is the magnitude of its final displacement from the origin?

Accepted Answer

$$13\ \mathrm{miles}$$

Question 12

Which of the following is the correct formula for the cross product magnitude $$|\vec{A} 	imes \vec{B}|$$?

Accepted Answer

$$|A||B|\sin	heta$$

Question 13

Given $$\vec{A} = 4\hat{i} + 3\hat{j}$$ and $$\vec{B} = -2\hat{i} + 3\hat{j}$$, what is the $$k-$$component of $$\vec{C} = \vec{A} 	imes \vec{B}$$?

Accepted Answer

$$18$$

Question 14

Which of the following numbers has 3 significant figures?

Accepted Answer

0.00320

Question 15

Rewrite $$0.00016 kg in $$scientific notation.

Accepted Answer

$$1.6 	imes 10$$^{-4}$$ kg

Question 16

If $$\vec{A}$$ and $$\vec{B}$$ are perpendicular vectors with $$|\vec{A}| = 3$$ and $$|\vec{B}| = 4$$, what is $$|\vec{A} + \vec{B}|$$?

Accepted Answer

$$5$$

Question 17

Which of the following is the correct SI unit for force?

Accepted Answer

Newton ($$\mathrm{N})$$

Question 18

A vector $$\vec{F} is$$ $$65\ \mathrm{m}$$ long, directed $$30.5^\circ$$ below the positive x-axis. What is $$F_x$$?

Accepted Answer

$$65 \cos(30.5^\circ)$$

Question 19

Which of the following is the correct rule for multiplying numbers in scientific notation?

Accepted Answer

Multiply the coefficients and add the exponents

Physics I: Units, Physical Quantities & Vectors – Mini Study Guide

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