Q: A car accelerates uniformly from rest to a speed of 20 m/s in 5 seconds. What is the car's acceleration?

$$a = \frac{20\ \text{m/s}}{5\ \text{s}} = 4\ \text{m/s}^2$$

Q: A projectile is launched at an angle $$\theta$$ with an initial speed $$v_0. $$Which equation gives the maximum height $$H$$ reached by the projectile?

$$H = \frac{v_0$^2 \sin^2$ \theta}{2g}$$

Q: A 10 kg box is pulled across a horizontal surface with a force of 50 N. If the coefficient of kinetic friction is 0.2, what is the acceleration of the box?

$$a = \frac{50\ \text{N} - (0.2 \times 10\ \text{kg} \times 9.8\ \text{m/s}^2)}{10\ \text{kg}} = 3.04\ \text{m/s}^2$$

Q: A spring with spring constant $$k = 200\ \text{N/m} is $$compressed by $$x = 0.1\ \text{m}. $$What is the potential energy stored in the spring?

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} \times 200 \times (0.1)^2$ = 1\ \text{J}$$

Question 1

A car accelerates uniformly from rest to a speed of 20 m/s in 5 seconds. What is the car's acceleration?

Accepted Answer

$$a = \frac{20\ 	ext{m/s}}{5\ 	ext{s}} = 4\ 	ext{m/s}^2$$

Question 2

Which of the following best describes the relationship between displacement, velocity, and acceleration in one-dimensional motion?

Accepted Answer

Velocity is the derivative of displacement with respect to time, and acceleration is the derivative of velocity with respect to time.

Question 3

A projectile is launched at an angle $$	heta$$ with an initial speed $$v_0. $$Which equation gives the maximum height $$H$$ reached by the projectile?

Accepted Answer

$$H = \frac{v_0$^2 \sin^2$ 	heta}{2g}$$

Question 4

A 10 kg box is pulled across a horizontal surface with a force of 50 N. If the coefficient of kinetic friction is 0.2, what is the acceleration of the box?

Accepted Answer

$$a = \frac{50\ 	ext{N} - (0.2 	imes 10\ 	ext{kg} 	imes 9.8\ 	ext{m/s}^2)}{10\ 	ext{kg}} = 3.04\ 	ext{m/s}^2$$

Question 5

Which of the following statements about Newton's Third Law is correct?

Accepted Answer

For every action, there is an equal and opposite reaction.

Question 6

A spring with spring constant $$k = 200\ 	ext{N/m} is $$compressed by $$x = 0.1\ 	ext{m}. $$What is the potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 200 	imes (0.1)^2$ = 1\ 	ext{J}$$

Question 7

A 2 kg object moving at 3 m/s collides elastically with a 1 kg object at rest. What is the velocity of the 2 kg object after the collision?

Accepted Answer

$$v_1$$' = \frac{($$m_1$$ - $$m_2$$)}{$$m_1$$ + $$m_2$$} $$v_1$$ = \frac{(2 - 1)}{2 + 1} 	imes 3 = 1\ 	ext{m/s}$$

Question 8

A solid disk of mass $$M$$ and radius $$R$$ rolls without slipping down an incline. What is its total kinetic energy at the bottom?

Accepted Answer

$$K = \frac{1}{2} M v^2$ + \frac{1}{2} I \$$omega^2$$ = \frac{1}{2} M v^2$ + \frac{1}{4} M v^2$ = \frac{3}{4} M v^2$

Question 9

A pendulum exhibits simple harmonic motion. Which equation gives its period for small angles?

Accepted Answer

$$T = 2\pi \sqrt{\frac{L}{g}}$$

Question 10

A fluid flows through a pipe that narrows from radius $$r_1 to$$ $$r_2. If $$the speed at $$r_1 is$$ $$v_1$$, what is the speed at $$r_2$$ according to the continuity equation?

Accepted Answer

$$v_2$$ = $$v_1$$ \frac{$$r_1^2$$}{$$r_2^2$$}$$

Question 11

Which principle explains why a boat floats in water?

Accepted Answer

Archimedes' principle: An object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced.

Question 12

A gas in a container is heated at constant volume. Which law relates the change in pressure to the change in temperature?

Accepted Answer

Gay-Lussac's law: $$\frac{P_1$}{T_1$} = \frac{P_2$}{T_2$}$$

Question 13

Which equation represents the work done by a gas during an isothermal expansion?

Accepted Answer

$$W = nRT \ln \left( \frac{V_f}{V_i} \right)$$

Question 14

A heat engine absorbs 500 J of heat and expels 300 J to the cold reservoir. What is its efficiency?

Accepted Answer

$$e = \frac{W}{Q_h} = \frac{500 - 300}{500} = 0.4$$

Question 15

A sound wave has a frequency of 440 Hz and travels at 330 m/s. What is its wavelength?

Accepted Answer

$$\lambda = \frac{v}{f} = \frac{330\ 	ext{m/s}}{440\ 	ext{Hz}} = 0.75\ 	ext{m}$$

Question 16

A train approaches a stationary observer at a speed of 30 m/s. If the train's horn emits a frequency of 500 Hz and the speed of sound is 340 m/s, what frequency does the observer hear?

Accepted Answer

$$f' = f \frac{v + v_o}{v - v_s} = 500 \frac{340}{340 - 30} = 500 \frac{340}{310} \approx 548\ 	ext{Hz}$$

Question 17

Which statement about entropy and the second law of thermodynamics is correct?

Accepted Answer

The entropy of an isolated system never decreases; it either increases or remains constant.

Question 18

A mass attached to a spring oscillates with amplitude $$A$$ and angular frequency $$\omega. $$What is the maximum speed of the mass?

Accepted Answer

$$v_{	ext{max}} = \omega A$$

Question 19

A student measures the density of a liquid as $$ho = 1.05\ 	ext{g/cm}^3. $$What is this value in SI units?

Accepted Answer

$$ho = 1.05 	imes 1000 = 1050\ 	ext{kg/m}^3$$

PHYSI 1201: General Physics I - Course Syllabus and Study Guide

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