Q1: [4] Knowing that in the next expression a is acceleration, v is speed, x is position and t is time, from a dimensional v x t

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1 The actual test contains 1 multiple choice questions and 2 problems. However, for etra eercise, this practice test includes12 questions and 3 problems. Questions: N.. Make sure that you justify your answers eplicitly on the space provided on this page in order to qualify for partial credit even when your choice is wrong. Q1: [4] Knowing that in the net epression a is acceleration, v is speed, is position and t is time, from a dimensional v t point of view, the equation a is t a) incorrect b) correct c) The dimensional validity of the epression depends on the unspecified system of coordinates. d) The dimensional validity of the statement depends on the unspecified standard of units. Q2: [4] Which of the following is a true statement? a) The components of a vector do not depend on the system of coordinates. b) vector s magnitude is negative if the force acts against the direction of motion. c) vector component of a vector can be equal to the vector. d) The angle giving the direction of a vector cannot be negative. e) None of the above. Q3: [4] When vectors and are added together they form a vector and their magnitudes satisfy the relationship = 2. Which of the following statements is true? a) They must be parallel to each other. b) They must be perpendicular on each other. c) They must oppose each other. d) They must be at 45º with respect to each other. e) They must have the same magnitudes. Q4: [4] What is the magnitude of the resultant R = 3 2 of the coplanar vectors = (3,2) and = (3,1)? a) Incomplete information b) 1 c) 3 d) 4 e) 5 Q5: [4] The adjacent motion diagram shows the positions at equal time intervals of four identical particles moving horizontally with zero or constant acceleration. Which of the four particles has an acceleration larger in magnitude? a) b) c) d) e) oth and have the same acceleration magnitude. Q6: [4] car travels due South slowing down. If the North direction is taken to be positive, and we denote Δ, v and a va,, its displacement, velocity and acceleration respectively, then a), v, a b), v, a c), v, a d), v, a e) None of the above. 1

2 Q7: [4] Which of the adjacent position vs. time graphs most likely represent the motion of the car described in the previous question? a) b) c) d) e) None of them. t t t Q8: [4] student drops a rubber ball vertically on a flat surface so the ball t bounces back into her hand. Which of the following is true about the average acceleration of the ball during the short instant when it is in contact with the floor? a) It is zero. b) It is non-zero, vertically upwards c) It is non-zero, vertically downwards d) It is the gravitational acceleration. e) ny of the answers above may be possible, depending on the velocity of the ball before it hits the floor. Q9: [4] What can you say about the following statement? The gravitational acceleration is always negative. a) True, since it points downwards. b) True, because it is opposite to the motion of an ascending object. c) False by popular vote, since we all know that g = 9.8 m/s 2 d) False, because it is always in the direction of motion of a freely falling object. e) epends on the system of coordinates Q1: [4] On the Moon, an object is thrown vertically upward with speed v = 2.5 m/s. It reaches a maimum height h = 1.9 m. Therefore, the gravitational acceleration on the Moon is: a) 9.8 m/s 2 b) 12 m/s 2 c) 1.6 m/s 2 d) e) Insufficient information Q11: [4] uddhist monk meditates at the edge of a cliff, holding one ball in each hand (since we all know that surreal postures deepen the insight). He simultaneously tosses one ball straight up with speed v and the other straight down, also with speed v. Which ball has the greater average speed during the 1-s interval after release? a) The ball thrown upward b) The ball thrown downward c) oth have the same average speed d) Insufficient information e) oesn t matter: on the path to Nirvana, up or down are irrelevant mundane illusions. Q12: [4] If the shadow of a ball moving in a circle of radius R with constant speed v is projected perpendicular unto a wall (say along a y-ais), it will oscillate with a velocity v y depending on time t as given by v y = vcos(ωt), where ω is some constant. Seeing how at time t = the shadow moved with maimum speed, which of the following gives the time dependency of the y-position of the shadow relative to the origin? a) y = R + v ω sin(ωt) b) y = R + v ω cos(ωt) c) y = v ω sin(ωt) d) y = v ω cos(ωt) e) None of the above. all R v y Shadow v y 2

3 Problems: In order to qualify for partial credit you have to provide at least a logical start toward a solution, even if it may be flawed. o not flood the space with obviously useless information. P1: The position-versus-time ( t) - graph below represents the one-dimensional motion of a particle. (N: On the trepresentation, the graph in the intervals - and - is parabolic and between - is a straight line. ssume zero slopes - in points and.) (m) 5. a) [3] alculate the acceleration a of the particle between points and b) [3] alculate the velocity v of the particle before point. 5. v (m/s) c) [3] alculate the acceleration a of the particle between points and. You may consider the speed equal on the two sides of point a (m/s 2 ) d) [8] Sketch the particle s motion graphs in the velocity vs. time (v-t) and then in the acceleration vs. time (a-t) representations. e) [3] ircle the interval(s) where the particle moves with negative velocity: [-] [-] [-] ircle the point(s) where the particle stopped. ircle the interval(s) where the particle moves with positive velocity. [-] [-] [-] ircle the interval(s) where the particle decelerates [-] [-] [-] ircle the interval(s) where the acceleration of the particle is zero [-] [-] [-] 3

4 (m) 1 P2: The velocity-versus-time (v-t) graph below represents the motion of a toy car starting at initial position = 8. m. a) [4] alculate the accelerations a, a, a of the car through the respective intervals, and v (m/s) b) [5] alculate the positions of the car in points, and a (m/s 2 ) c) [8] Sketch the particle s motion graphs in the position vs. time (-t) and then in the acceleration vs. time (a-t) representations. d) [3] Each dot on the motion diagrams below marks the location of a moving particle at equal time intervals. Which motion diagram is the closest representation for the motion of the car in our problem? None of the above, since our car doesn t move in only one direction. 4

5 P3: car, initially at rest in point, moves along a straight line interval - with constant acceleration a = 2.5 m s 2 until it reaches point after a time t = 8. s. In point, the driver notices a vertical wall located in point, at position = 16 m, so he starts decelerating uniformly at a rate a s until the car stops after a time interval Δt s = 5. s. t = = v = a = 2.5 m s 2 t = 8. s =? v =? Δt s = 5. s d s =? a s =? stop s =? v s = = 16 m a) [5] What is the position of the car in point relative to the starting point? b) [5] Find the velocity v in point both in m s and km hour. c) [8] On the diagram, I represented the stop point of the car ahead of the wall. However, this is just a tentative illustration for you to see how to set up your problem. Given the data in the problem, can the driver actually stop before hitting the wall in the given time t s? d) [5] What is the acceleration a s of the car in the stopping interval? (m) e) [7] Use the adjacent chart to represent the car s position versus time. The parabolas don t have to be perfect, but qualitatively correct stop 5

6 P4: rocket rises vertically, from rest. Its engine works for a time t 1 = 5. s then it runs out of fuel. The time dependent velocity of the rocket while the engine works is given by v(t) = t + t 3, where = 2.3 m/s 2 and =.46 m/s 4. fter the engine stops, the rocket moves freely. f) [4] Find out symbolical epressions (in terms of, and time t) for the vertical position and acceleration as functions of time until the rocket runs out of fuel. Useful derivative and antiderivative (n is a constant): y g) [4] alculate numerically the rocket s altitude y 1, velocity v 1 and acceleration a 1 at the moment t 1 when the engine runs out of fuel (that is, at the end of the acceleration interval). fuel out h) [4] fter it runs out of fuel, the rocket is under the sole effect of its weight. alculate the maimum altitude y 2 with respect to the ground subsequently reached by the rocket, and the total time t 2 it takes to reach it, relative to the startup time. i) [4] alculate the time it takes the rocket to fall back to the ground (from the maimum altitude). ground y (m) 4 j) [4] The adjacent graph represents the position of the rocket until the fuel runs out. omplete the graph by sketching the curve representing the position of the rocket between the moment when its fuel runs out and when it returns back to the ground. (Notice that the graph shows you what you have to obtain eplicitly in part (b) for the altitude at time t 1 ) t