25. Consider n moles of an ideal gas being compressed isothermally at absolute temperature T from an initial volume V₁ to a final volume V₂. The R and ke are, respectively, universal gas constant and Boltzmann constant. What is the change in entropy?
(A) nR In (V₂/V₁)
(B) nRT ln (V₂/V₁)
(C) nkB In (V₂/V₁)
(D) nk_BT In (V₂/V₁)
(E) nk_B (V₂-V₁.)

1.Cart A, of mass m, starts from rest and travels in a straight line with acceleration a. It traverses a ance x in time t. Cart B, of mass 4m, starts from rest and travels in a straight Iine with acceleration a/2. At time t it has traversed the distance (A) x/4 (B) x/2 (C) x (D) 2x (E) 4x

2. An automobile traveling along a straight road increases its speed from 30.0 m/s to 50.0 m/s in a nce of 180 m. If the acceleration is constant, how much time elapses while the au distance? (A) 6.00 s (B) 4.50 s (C) 3.60 s (D) 4.00 s (E) 9.00 s

3. A particle moves in the xy plane with a constant acceleration given by a = -m/s2. At t = 0, its position and velocity are m/s, respectively. Here, t and j are unit vectors ng x and y directions, respectively. What is the distance from the origin to the pa 2.0 s? (A) 6.4 m (B) 10 m (C) 8.9 m (D) 2.0 m (E) 6.2 m

4. Two balls, projected at different times so they don't collide, have trajectories A and B, as shown ow. Ignore the air resistance and friction. Which of the following is necessarily true? (A) The initial velocity of ball B is greater than that of ball A. (B) The initial velocity of ball A is than that of ball B. (C) Ball A is in the air for a longer time than ball B. (D) B for a longer time than ball A.(E) Ball B has a greater acceleration th

5. lf M= 6.0kg, what is the tension in string 2? Note that the acceleration due to gravity g=9.8m/s2. (A) 39 N (B) 35 N (C) 29 N(D) 44 N (E) 51 N

6.The horizontal surface on which the objects slide is frictionless. If M = 1.0 kg and the magnit rce of the small block on the large block is 5.2 N, determine F. (A) 6.0 N (B) 9.0N (C)4.8N(D)4.1N(E)7.8 N

7.The total force needed to drag a box at constant speed across a surface with coefficient of kinetic friction μ is least when the force  is applied at an angle θ such that (A) sinθ = μ(B) cosθ=μ(C) tan θ=μ(D) cotθ=μ(E) secθ =μ

8. Arace car traveling at 100 m/s enters an unbanked turn of 400 m radius. The coeffic ion between the tires and the track is 1 .1. The track has both an inner and an outer statement is correct? (A) The race car will crash into the outer wall. (B) The race car will crash into the inner wall. (C) The car will stay in the center of the track. (D) The car will stay in the er of the track if the driver speeds up. (E) The car would stay in the center of the radius were reduced to 200 m.

9.A certain pendulum consists of a 1.5-kg mass swinging at the end of a string (length=2.0m).At the lowest   point in the swing the tension in the string is equal to 20 N. To what maximur e this lowest point will the mass rise during its oscillation? Note that the accele gravity g = 9.8 m/s2. (A) 77 cm (B) 50 cm (C) 63 cm (D) 36 cm (E) 95 cm

10. Two equal masses are raised at constant velocity by ropes that run over pulleys, as shown below. B is raised twice as fast as mass A. The magnitudes of the forces exerted by masses A and B are, respectively, FA and FB, while the power supplied for each is PA and PB. Which statement is correct? (A) FB =FA；PB=PA.(B) FB = FA； PB=2 PA.(C) FB=2 FA；PB=PA. (D) FB = 2 FA； PB = 2 PA. (E) PA = FA； PB = FB.

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