SPH3U Review questions (Ch 1) 1. A jet is flying with a speed of 252 km/h when it lands on an aircraft carrier and hooks onto a steel cable that brings it to a stop in a distance of 95 m. Determine the average acceleration of the jet while it is stopping. 2. The following d-t graph represents an object with an initial velocity of 6 m/s and constant acceleration. a) Determine the instantaneous velocity at 0.7 seconds. b) Determine the average velocity over the entire 4 second time interval. c) Create an accurate graph of velocity vs. time for the entire 4 second time interval. 3. The following d-t graph represents an object that begins at rest then accelerates at a constant rate. a) Determine the position, velocity, and acceleration at exactly 1.5 seconds. b) Determine the average velocity from 1 second to 3.5 seconds. c) Create an accurate graph of velocity vs. time for the entire 4 second time interval. 4. Determine the average velocity and total displacement for each graph. 5. A sprinter completes the 100 m dash in 12 seconds. A nearby physics teacher estimates that the sprinter accelerated for the first 2 seconds of the race before maintaining a constant velocity for the remainder of the race. Determine (a) the final velocity and (b) the initial acceleration. 6. The following velocity vs. time graph represents the motion of a sports car accelerating during a performance test. Determine its average velocity and total displacement for the 6 second time interval. 7. The following graph represents an object experiencing constant acceleration. Determine: a) the velocity at 2.6 seconds b) when the velocity equals 9 m/s c) graphs of velocity vs. time and acceleration vs. time 8. Calculate the acceleration of a sailboat that speeds up from 5.5 m/s to 12 m/s over a distance of 48 ft. 9. A sprinter completes the 100 m dash in 14 seconds. A nearby physics teacher estimates that the sprinter accelerated for the first 3.5 seconds of the race before maintaining a constant velocity for the remainder of the race. Determine (a) the final velocity and (b) the initial acceleration. 10. Create graphs of position, velocity, and acceleration vs. time for a snowboarder who coasts at a constant velocity of 54 km/h [forward] for 2.0 seconds before sliding to a stop in 3.0 seconds. 11. A student was provided with the following graphs and asked to calculate the average velocity shown in each graph. The student drew the dashed lines and calculated their slopes. Did the student provide correct answers? Explain your reasoning for each graph. Therefore, the average 12 = 1.2 m/s velocity is 1.2 m/s. 10 18 = 1.8 m/s 10 Therefore, the average velocity is 1.8 m/s. 12. Consider the following motion graphs (each graph represents the motion of a different object). a) b) c) d) Describe the motion represented by each graph. Determine the total displacement represented by each graph. Determine the average velocity represented by each graph. Determine the average acceleration represented by each graph. 13. Calculate the slope of each graph and describe what it represents in each case. Answers: 1. acceleration = – 26 m/s2 2. a) 2.5 m/s b) – 4 m/s 3. a) d = 12.5 m v = 7.5 m/s c) v-t graph shown below a = 5 m/s2 b) v = 11.2 m/s 3. c) The following graph represents the velocity (in m/s) vs. time (in s): 4. v-t graph: v = 26.8 m/s 5. final velocity = 9.1 m/s ∆ d = 134 m d-t graph: acceleration = 4.5 m/s2 6. average velocity = 70 km/h total displacement = 117 m v = 9m/s ∆ d = 27 m 7. a) 1.9 m/s b) t = 0.57 s c) v-t and a-t graphs shown below 8. acceleration = 3.9 m/s2 9. final velocity = 8.2 m/s acceleration = 2.3 m/s2 10. The following d-t, v-t and a-t graphs represent the motion of the snowboarder in m, m/s and m/s/s: 11. The first answer is correct because average velocity is the slope of a position vs. time graph. The second answer is incorrect because the slope of a velocity vs. time graph represents acceleration NOT velocity. The best approach is to use the average velocity for each section of the v-t graph to calculate displacement. Then divide the total displacement by the total time. 12. a) The first graph shows an object travelling with a constant velocity of 6 m/s [forward] for 4 seconds, then at rest for 1 second at a position of 24 m, then 5 m/s [backward] for 2 seconds. The second graph shows an object accelerating at a constant rate of 6 m/s/s for 3 seconds, then travelling with a constant velocity of 18 m/s for 4 seconds, then accelerating at 4 m/s/s for 3 seconds to reach a final velocity of 30 m/s [forward]. b) Displacement is 14 m for the position vs. time graph and 171 m for the velocity vs. time graph. c) Average velocity is 2 m/s for the d-t graph and 17.1 m/s for the v-t graph. d) The average acceleration is –1.57 m/s/s for the d-t graph and 3 m/s/s for the v-t graph. 13. The slope of the graph of position vs. time is 1.75 m/s. This represents an average velocity. The slope of the graph of velocity vs. time is 1.25 m/s/s. This represents an average acceleration.

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