31. The motion of a car can be described by the equation x(t)=15t-2t², where x and t are in meters and seconds, respectively. What is the acceleration of the car after 3 seconds?
(A) 27 m/s²
(B) 12 m/s²
(C) 4 m/s²
(D) -4 m/s²
(E) -12 m/s²

32. A solid cylinder and a thin hoop of the same mass m and radius R are released from rest (at the same moment) at the top of an incline. If they roll without slipping, which object will have a greater translational velocity at the bottom of the incline? (A) The solid cylinder. (B) The thin hoop. (C) They will have the same velocity. (D) The velocity depends on the angle of the incline. (E) None of the above.

33. Two blocks of equal mass m are connected by a spring with the spring constant k and placed on a frictionless surface. If the right block is given an initial velocity v while the left block is at rest, what is the minimum kinetic energy of the system during the subsequent oscillation? (A) 0 (B) (1/8)mv2 (C) (1/4)mv2 (D) (1/2)mv2 (E) mv2

34. An ice cube is floating in a glass of pure water. The system remains at 0°C as the ice melts. How does the water level change? (A) It increases. (B) It decreases. (C) It remains exactly the same. (D) It depends on the size of the ice cube. (E) None of the above.

35. A cylindrical water tank with a height of 1 meter (m) and a base area of 0.1 m2 contains 50 kg of pure water. A mass of 10 kg of salt is added to the water and allowed to dissolve completely. What is the gauge pressure at the bottom of the tank? (Assume gravitational acceleration g = 10 m/s2 for simplicity). [unit: pascal (Pa)] (A) 400 Pa (B) 600 Pa (C) 4000 Pa (D) 5000 Pa (E) 6000 Pa

36. Two people with masses of 60 kg and 80 kg are initially at rest on a frictionless level surface, separated by a distance of 20 meter (m). They both pull on opposite ends of a massless rope to move towards one another. If the total distance between them decreases by 14 m, how far has the 80-kg person traveled? (A) 10 m (B) 8 m (C) 6.4 m (D) 6 m (E) 3.6 m

37. A pulley with a radius of 3.0 cm and a rotational moment of inertia of I = 9.0 × 10-3 kg·m2 is suspended from a ceiling. A massless, non-slip rope passes over the pulley, supporting two blocks with masses of 1.0 kg and 3.0 kg. Determine the total kinetic energy of the system at the instant the 1.0 kg block reaches a speed of 1.0 m/s. [unit: joule (J)] (A) 1.0 J (B) 2.0 J (C) 7.0 J (D) 14 J (E) 28 J

38. We would like to estimate the energy consumed to run the left ventricle. Given that the rate at which the left ventricle does mechanical work is 1.046 watt. Nevertheless, the efficiency of converting the metabolic energy into mechanical energy is approximately 25%. Calculate the energy consumed to run the left ventricle per day. [1 calorie (cal) = 4.184 joules (J)] (A) 5.40 × 104 (cal/day) (B) 4.18 × 104 (cal/day) (C) 2.62 × 104 (cal/day) (D) 8.64 × 104 (cal/day) (E) 9.62 × 104 (cal/day)

39. The human brain is approximately 56 cm above the heart. The average blood pressure in the major arteries near the heart is 95 mm-Hg. Assume that the density of blood is the same as that of water. What is the blood pressure in the brain in major arteries? [1mm-H2O = 0.0736 mm-Hg] (A) 136.2 mm-Hg (B) 95.0 mm-Hg (C) 53.8 mm-Hg (D) 42.8 mm-Hg (E) 33.2 mm-Hg

40. Atherosclerosis occurs when a deposit forms on an arterial wall. Suppose that the cross-sectional area becomes A2/A1=1/4, and this leads to a faster blood flow speed. The pressure in the region without plaque is P1, and the pressure in the region with plaque is P2. Use Bernoulli's equation to calculate the pressure drop P2 − P1. The blood density is ρ and the blood speed in the region without plaque is v1. (A) (B) (C) (D) (E) None of the above

41. A perfect Carnot engine operates between a hot reservoir at 800 K and a cold reservoir at 400 K. If the engine performs 200 joule (J) of work in each cycle, how much heat is exhausted to the cold reservoir in each cycle? (A) 800 J (B) 600 J (C) 400 J (D) 200 J (E) 100 J

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