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Unformatted text preview: Answer key for first exam version B 1 1. The net displacement ~ AC is- 5 meters, and this displacement is accomplished in 28 seconds. Thus the average velocity ~v AC = ~ AC/ 28 seconds = -0.179 m/s. The negative sign indicates that the direction of the average velocity is the negative x direction. Answer = A (-0.179 m/s) 77% answered correctly 2. The total distance traveled (from A to B to C) is 5 + 10 + 10 = 25 meters, in 28 seconds. So the average speed is 25 / 28 = 0 . 893 m/s. Answer = D (0.893 m/s) 61% answered correctly 3. An object can have momentarily zero velocity but non-zero acceleration, such as a ball thrown vertically upwards at the highest point of its motion. A changing velocity must mean a non-zero acceleration, which could be constant or varying in time. An object could be moving East with an East acceleration, meaning that the speed of the object is increasing. Conversely, an object moving East with a West acceleration is decelerating, meaning its speed is decreasing. An object with a constant non-zero velocity cannot have any acceleration, either constant or changing. Answer = D 72% answered correctly 4. This is a one-dimensional motion problem with constant acceleration a y =- g =- 9 . 8 m/s 2 . We have y = 70, with a choice of origin at ground level. Also, v = +31 . 9 m/s. To find out when the ball hits the ground we use the position kinematic equation with constant acceleration: y ( t ) = y + v t- 1 2 gt 2 and solve for the time t value such that y ( t ) =- 70 meters. This results in a quadratic equation for which the positive (physically appropriate) solution is 8.2 seconds. Answer = B (8.2 s) 86% answered correctly 5. Vector ~ A = (5 . 7 ,- 3 . 6) and ~ B = (- 9 . 8 ,- 6 . 5). Then the difference ~ D = ~ B- ~ A = (- 15 . 5 ,- 2 . 9). So the magnitude D = q (- 15 . 5) 2 + (- 2 . 9) 2 = 15 . 8. Answer = C (16) 76% correctly answered Answer key for first exam version B 2 6. Rotating a vector changes its direction. One cannot add a scalar to a vector, although one can multiply a vector by a scaler. Only vectors of the same mag- nitude can be summed to zero (they would be anti-parallel). A vector with a non-zero component must have a magnitude of at least the size of that compo- nent. The magnitude of a vector is independent of the coordinate system usednent....
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- Spring '08