Q: A car travels 60 miles per hour. Convert this speed to meters per second. (1 mile = 1609 m, 1 hour = 3600 s)

$$60 \times \frac{1609}{3600} = 26.8 m/s$$

Q: A vector $$\vec{A}$$ has components $$A_x = -6$$, $$A_y = 8. $$What is the direction of $$\vec{A}$$ with respect to the positive x-axis?

$$\tan$$^{-1}$$\left(\frac{8}{-6}\right) = 126.9^\circ$$

Question 1

Which of the following is a fundamental SI unit?

Accepted Answer

Kelvin (K)

Question 2

A student measures the length of a table as 1.250 meters. How many significant figures are in this measurement?

Accepted Answer

4

Question 3

Which of the following quantities is a vector?

Accepted Answer

Displacement

Question 4

A car travels 60 miles per hour. Convert this speed to meters per second. (1 mile = 1609 m, 1 hour = 3600 s)

Accepted Answer

$$60 	imes \frac{1609}{3600} = 26.8 m/s$$

Question 5

Which of the following is the correct dimensional formula for energy?

Accepted Answer

$$[E] = ML$$^{2}$$T^{-2}$

Question 6

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

Accepted Answer

$$\sqrt{3^2$ + 4^2$} = 5$$

Question 7

Which law states that the sum of two vectors is independent of the order in which they are added?

Accepted Answer

Commutative Law

Question 8

A force $$\vec{F} of$$ $$10 N $$acts at an angle of $$30^\circ to $$the horizontal. What is the horizontal component of the force?

Accepted Answer

$$10 \cos(30^\circ) = 8.66 N$$

Question 9

Which of the following is NOT a correct rule for significant figures?

Accepted Answer

Leading zeros in a number with a decimal point are significant.

Question 10

A vector $$\vec{A} is $$multiplied by a negative scalar $$-3. $$What happens to the vector?

Accepted Answer

Its magnitude triples and its direction reverses.

Question 11

Given vectors $$\vec{A} = 2\hat{i} + 3\hat{j}$$ and $$\vec{B} = 4\hat{i} - 5\hat{j}$$, what is $$\vec{A} \cdot \vec{B}$$?

Accepted Answer

$$(2)(4) + (3)(-5) = 8 - 15 = -7$$

Question 12

If the angle between two vectors $$\vec{A}$$ and $$\vec{B} is$$ $$90^\circ$$, what is their scalar (dot) product?

Accepted Answer

$$0$$

Question 13

A vector $$\vec{A}$$ has components $$A_x = -6$$, $$A_y = 8. $$What is the direction of $$\vec{A}$$ with respect to the positive x-axis?

Accepted Answer

$$	an$$^{-1}$$\left(\frac{8}{-6}ight) = 126.9^\circ$$

Question 14

Which of the following is the correct expression for the cross product $$\vec{A} 	imes \vec{B} in $$terms of components?

Accepted Answer

$$(A_yB_z - A_zB_y)\hat{i} + (A_zB_x - A_xB_z)\hat{j} + (A_xB_y - A_yB_x)\hat{k}$$

Question 15

A right-handed coordinate system is used in physics. Which rule helps determine the direction of the cross product $$\vec{A} 	imes \vec{B}$$?

Accepted Answer

Right-hand rule

Question 16

A sphere of plutonium-237 has a mass of $$60 kg $$and a density of $$19.3 g/cm$^3. $$What is the radius of the sphere in centimeters? (Use $$V = \frac{4}{3}\pi r^3$ and $$\rho = \frac{m}{V}$$)

Accepted Answer

$$r = \left(\frac{3m}{4\pi \rho}\$$right)^{1/3}$$, with m = 60000$ g, $$\rho = 19.3$$ g/cm^3$, so r$$ \approx 17.5$$ cm

Question 17

Which of the following is a correct example of dimensional analysis for velocity?

Accepted Answer

$$[v] = LT$$^{-1}$$

Question 18

If $$\vec{A} = 4\hat{i} + 7\hat{j}$$ and $$\vec{B} = 5\hat{i} - 2\hat{j}$$, what is the magnitude of $$\vec{A} - \vec{B}$$?

Accepted Answer

$$\sqrt{(4-5)^2$ + (7-(-2))^2$} = \sqrt{1^2$ + 9^2$} = \sqrt{82} \approx 9.06$$

Question 19

Which prefix represents $$10^{-9} in SI $$units?

Accepted Answer

nano

Units, Physical Quantities, and Vectors – Foundations of Physics

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