Particle A has less mass than particle B. Both are pushed forward across a frictionless surface by equal forces for 1 s. Both start from rest. a. Compare the amount of work done on each particle. That is, is the work done on A greater than, less than, or equal to the work done on B? Explain. b. Compare the impulses delivered to particles A and B. Explain. c. Compare the final speeds of particles A and B. Explain. c. Compare the final speeds of particles A and B. Explain.

Study the entries and answer the question that follows.

The roots grad and gress mean "step."

The roots ced and cess mean "go."

The prefix de- means "down."

The prefix pro- means "forward."

The prefix re- means "back."

The prefix di- means "apart" or "away from."

The prefix trans- means "across" or "through."

The prefix se-means "away." In the $1860$s, the Confederate States tried to ______________ (literally, "go away") from the Union.

The gas-phase reaction between hydrogen and iodine

$$\mathrm{H}_2(g)+\mathrm{I}_2(g) \rightleftharpoons 2 \mathrm{HI}(g)$$

proceeds with a rate constant for the forward reaction at $700^{\circ} \mathrm{C}$ of $138 \mathrm{~L} / \mathrm{mol} \cdot \mathrm{s}$ and an activation energy of $165 \mathrm{~kJ} / \mathrm{mol}$. (a) Calculate the activation energy of the reverse reaction given that $\Delta H_{\mathrm{f}}^{\circ}$ for $\mathrm{HI}$ is $26.48 \mathrm{~kJ} / \mathrm{mol}$ and $\Delta H_{\mathrm{f}}{ }^{\circ}$ for $\mathrm{I}_2(\mathrm{~g})$ is $62.44 \mathrm{~kJ} / \mathrm{mol}$. (b) Calculate the rate constant for the reverse reaction at $700^{\circ} \mathrm{C}$. (Assume $\mathrm{A}$ in the equation $k=\mathrm{Ae}^{-E_{\mathrm{a}} / R T}$ is the same for both forward and reverse reactions.) (c) Calculate the rate of the reverse reaction if the concentration of $\mathrm{HI}$ is $0.200 \mathrm{M}$. The reverse reaction is second-order in HI.

Write the solution of the problem $u_{t t}=u_{x x}$ for $-\infty<x<\infty, t>0$ and $u(x, 0)=f(x), u_{t}(x, 0)=0$ for $-\infty<x<\infty$ as a sum of a forward and a backward wave. Graph the initial position function and then graph the solution at selected times, showing the wave as a superposition of a wave moving to the right and a wave moving to the left.

$$f(x)=\left\{\begin{array}{ll} 1-x^{2} & \text { for }|x| \leq 1 \\ 0 & \text { for }|x|>1 \end{array}\right.$$

A car and driver with a combined mass of $1.5 \times 10^3 \mathrm{~kg}$ experience a forward force of $7.67 \times 10^3 \mathrm{~N}$ and forces of friction and drag of $7.7 \times 10^2 \mathrm{~N}$. What is the acceleration of the car and driver? (a) $4.1 \mathrm{~m} / \mathrm{s}^2$ (b) $4.6 \mathrm{~m} / \mathrm{s}^2$ (c) $5.1 \mathrm{~m} / \mathrm{s}^2$ (d) $5.6 \mathrm{~m} / \mathrm{s}^2$

The Latin root -jec-means "thro w." This root is found in many scientific words, such as conjecture, which means "to guess by 'throwing' facts or inferences together."
Choose the letter of the best definition for the given word below. "eject": a. to "throw" forward b. to "throw" into c. to "throw" out of d. object designed to be "thrown" or shot e. path along which an object is "thrown" f. "thrown" away; hopeless g. state of being "thrown" down; depression h. "throw" back at

On a cold winter morning, a child sits on a sled resting on smooth ice. When the $9.75-\mathrm{kg}$ sled is pulled with a horizontal force of $40.0 \mathrm{~N}$, it begins to move with an acceleration of $2.32 \mathrm{~m} / \mathrm{s}^2$. The $21.0-\mathrm{kg}$ child accelerates too, but with a smaller acceleration than that of the sled. Thus, the child moves forward relative to the ice, but slides backward relative to the sled. Determine the acceleration of the child relative to the ice.

A 275-mL flask contains pure helium at a pressure of 752 torr. A second flask with a volume of 475 mL contains pure argon at a pressure of 722 torr. If we connect the two flasks through a stopcock and we open the stopcock, what is the partial pressure of each gas and the total pressure?

The airplane is at the beginning of its takeoff run. Its weight is $1000 \mathrm{lb}$, and the initial thrust $T$ exerted by its engine is $300 \mathrm{lb}$. Assume that the thrust is horizontal, and neglect the tangential forces exerted on the wheels. (a) If the acceleration of the airplane remains constant, how long will it take to reach its takeoff speed of $80 \mathrm{mi} / \mathrm{h}$ ? (b) Determine the normal force exerted on the forward landing gear at the beginning of the takeoff run.

A girl riding a bicycle at 2.0 m/s throws a tennis ball horizontally forward at a speed of 1.0 m/s from a height of 1.5 m. At the same moment, a boy standing on the sidewalk drops a tennis ball straight down from a height of 1.5 m. If air resistance is disregarded, which ball will have a greater speed (relative to the ground) when it hits the ground? A. the boy’s ball, B. the girl’s ball, C. neither, D. The answer cannot be determined from the given information.

Consider the equation for acetic acid plus water. Use the table "Relative Strengths of Acids and Bases," earlier in this chapter, to answer the questions below.

$$\mathrm{CH}_3 \mathrm{COOH}+\mathrm{H}_2 \mathrm{O} \rightleftarrows \mathrm{CH}_3 \mathrm{COO}^{-}+\mathrm{H}_3 \mathrm{O}^{+}$$

a. Compare the strength of the two acids.

b. Compare the strength of the two bases.

c. Which direction, forward or reverse, is favored for this reaction?

A car is moving forward slowly and speeding up. A student claims "the car exerts a force on itself" or "the car's engine exerts a force on the car." Argue that this idea cannot be accurate and that friction exerted by the road is the propulsive force on the car. Make your evidence and reasoning as persuasive as possible. Is it static or kinetic friction? Suggestions: Consider a road covered with light gravel. Consider a sharp print of the tire tread on an asphalt road, obtained by coating the tread with dust

The wheels of a midsize car exert a force of 2100 N backward on the road to accelerate the car in the forward direction. If the force of friction including air resistance is 250 N and the acceleration of the car is $1.80\ \mathrm{m} / \mathrm{s}^{2},$ what is the mass of the car plus its occupants? Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton's laws of motion. For this situation, draw a free-body diagram and write the net force equation.

The Latin root -jec-means "thro w." This root is found in many scientific words, such as conjecture, which means "to guess by 'throwing' facts or inferences together."
Choose the letter of the best definition for the given word below. "inject": a. to "throw" forward b. to "throw" into c. to "throw" out of d. object designed to be "thrown" or shot e. path along which an object is "thrown" f. "thrown" away; hopeless g. state of being "thrown" down; depression h. "throw" back at