5. A car of mass m moving at a speed \( v_1 \) collides and couples with the back of a truck of mass 2m moving initially in the same direction as the car at a lower speed \( v_2 \). What is the speed \( v_f \) of the two vehicles immediately after the collision?
(A)\( v_f = \frac{2}{3}(v_1 - 2v_2) \)
(B)\( v_f = \frac{2}{3}(v_1 + v_2) \)
(C)\( v_f = \frac{1}{3}(v_1 - 2v_2) \)
(D)\( v_f = \frac{1}{3}(v_1 + 2v_2) \)

(E)\( v_f = \frac{1}{2}(v_1 + v_2) \)

1. A particle moves along the y axis. Its position is given by the equation \( y(t) = 2 + 3t - 4t^2 \), with y in meters and t in seconds. What's its position when it changes direction?(A)2.56 m(B)1.28 m(C)4.23 m(D)2.12 m(E)3.84 m

2. A particle moves along a straight line starting at t = 0. Its position is given by the equation \( x(t) = 75t - 1.0t^3 \), where t is in seconds. When it stops (v=0), its acceleration is:(A)0(B)-73 m/s²(C)-30 m/s²(D)-9.8 m/s²(E)49 m/s²

3. A single closed loop of chain of mass m and length l rests on the surface of a smooth, frictionless cone. The chain lies in a horizontal plane. The half-angle of the cone is α. What's the tension in the chain?(A)\( T = \frac{mg}{\tan\alpha} \)(B)\( T = \frac{mg}{2\pi} \)(C)\( T = mg \)(D)\( T = \frac{mg}{2\pi\cot\alpha} \)(E)\( T = \frac{mg}{2\pi\tan\alpha} \)

4. If the net work done by external forces on a particle is zero, which of the following statements about the particle must be true?(A)Its velocity is zero.(B)Its velocity is decreased.(C)Its velocity is unchanged.(D)Its speed is unchanged.(E)More information is needed.

6. Objects A and B interact with each other via both conservative and nonconservative forces. Let \( K_A \) and \( K_B \) be the kinetic energies, U be the potential energy, and \( E_{int} \) be the internal energy. If no external agent does work on the objects then:(A)\( K_A + U \) is conserved(B)\( K_A + U + E_{int} \) is conserved(C)\( K_A + K_B + E_{int} \) is conserved(D)\( K_A + K_B + U \) is conserved(E)\( K_A + K_B + U + E_{int} \) is conserved

7. A uniform stick of length l is pivoted at one end, and released from rest in a horizontal position. How long will it take for it to swing down to the vertical position?(A)\( 1.311\sqrt{\frac{l}{3g}} \)(B)\( 2.622\sqrt{\frac{l}{3g}} \)(C)\( 1.311\sqrt{\frac{l}{2g}} \)(D)\( 2.622\sqrt{\frac{l}{2g}} \)(E)\( 2.622\sqrt{\frac{l}{g}} \)

8. The displacement of a string is given by \( y(x,t) = y_m \sin(kx + \omega t) \). The speed of the wave is(A)\( \frac{2\pi k}{\omega} \)(B)\( \frac{\omega}{k} \)(C)\( \omega k \)(D)\( \frac{2\pi}{k} \)(E)\( \frac{k}{2\pi} \)

9. A diffraction-limited telescope, designed for use in space, has an aperture of 1 m and a focal length of 20 m. At the focus in a TV detector whose "resolution element" size is \( 10^{-5} \) m. At what wavelength is the telescope optimal in the sense that \( 10^{-5} \) m corresponds to the diffraction limit?(A)4,000 Å(B)2,000 Å(C)1,000 Å(D)3,000 Å(E)5,000 Å

10. An ideal monatomic gas at room temperature is adiabatically decompressed so that the final volume is 8 times the original. What's the final temperature?(A)55 K(B)75 K(C)150 K(D)85 K(E)100 K

11. How long would it take for a 1000 W heater to melt 1.00 kg of ice at −20.0°C, assuming all the energy from the heater is absorbed by the ice?(A)4.18 s(B)41.8 s(C)5.55 min(D)6.25 min(E)38.4 min

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