# 8.4.1.C. YEAR 11 HSC PHYSICS 8.4 MOVING ABOUT Worksheet Velocity Time Graphs. Set 1 Drawing velocity-time graphs

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1 YEAR 11 HSC PHYSICS 8.4 MOVING ABOUT Worksheet Velocity Time Graphs C Set 1 Drawing velocity-time graphs 1. The table below is a table of data from an experiment measuring the! variation of speed with time for a car. Time (s) Speed (ms -1 ) a) Graph the data on a speed-time graph.! b) Find the speed of the car at 35.0 s.! c) Find how long the car took to decelerate from 30.0 to 10.0 m s -1. d) Determine the acceleration at 70.0 s.! e) How far did the car travel during the time s? Page 1

2 Set 2 Definitions and meanings 2. Contrast the terms uniform motion and non-uniform motion. 3. What is the gradient of a graph? Identify the information the gradient!gives us in displacement-time and velocitytime graphs. 4. Outline why we normally place time along the horizontal axis of a! motion graph. 5. Describe how displacement is determined from a graph. 6. Explain why we use a 'line of best fit' with a graph. Set 3 - Interpreting velocity-time graphs 7. The diagram shows the velocity-time graph for a car travelling in a!straight line along a road. a) Calculate the acceleration between t = 0 s and t = 2.0 s..... Page 2

3 b) Calculate the acceleration between t = 2.0 s and t = 5.0 s. c) Calculate the displacement between t = 0 s and t = 5.0 s. 8. The graph shows a velocity-time graph for a student moving in a straight line. From the graph:! a) calculate the acceleration between:! (i) t = 0 s and t = 3.0 s. (ii) t = 3.0 s and t = 6.0 s! (iii) t = 6.0 s and t = 9.0 s! (iv) t = 9.0 s and t = 12.0 s b) calculate the displacement during the!following time intervals:! (i) t = 0 s and t = 6.0 s (ii) t = 0 s and t = 9.0 s (iii) t = 0 s and t = 12.0 s Page 3

4 c) calculate the distance travelled between t = 0 s and t = 12.0 s d) sketch the displacement-time graph for! the motion. 9. The graph shows a velocity-time graph for a soccer player moving!in a straight line during part of a match.! a) Calculate the acceleration between t = 0 s!and t = 2.0 s.! b) Calculate the instantaneous acceleration! at t = 8.0 s.! c) Calculate the acceleration between t = 4.0 s! and t = 7.0 s.! d) Calculate the instantaneous acceleration!at t = 9.0 s.! Page 4

5 e) Determine the distance the player travels!between t = 0 s and t = 6.0 s.! f) What is the total distance covered by the!player between t = 0 s and t = 14.0 s?! g) What is the displacement between t = 0 s and t = 14.0 s? 10. A motor bike moves in a straight line, accelerating uniformly at! 3.0 ms -2 for 10.0 s, moving at a constant speed of 30.0 m s -1 for a!further 20.0 s, and finally decelerating at a constant rate of 2.0 ms -2!until coming to rest. Draw a velocity-time graph for this motion and!hence determine the total distance travelled during the entire journey. 11. The graph shows at speed-time graph of the motion of a cyclist.! a) Determine the speed at 5.0 s. b) At what time is the speed 4.0 m s -1? c) Determine between which times the speed is constant.! Page 5

6 d) Calculate the acceleration at 4.0 s.! e) What distance has the cyclist travelled between 3.0 s and 5.0 s? Page 6

7 Answers Set 1 Drawing velocity-time graphs 1 a) See graph below. b) Approximately 32 ms -1 c) 16 s d) -1.3 ms -1 e) 2350 m Set 2 Definitions and meanings 2 Uniform motion occurs when the magnitude of the acceleration is constant. Non-uniform motion occurs when the magnitude of the acceleration is not constant. 3 The gradient of the graph is the gradient of a tangent drawn at any given point along the line or curve. The gradient of a displacement-time graphs is the velocity of an object at a given time while the gradient of a velocity-time graph is the acceleration of the object at any given time. 4 Time is the independent variable and it is usual to graph the independent variable on the x-axis. 5 In the case of a displacement-time graph, displacement is read as the value on the vertical axis. In the case of a velocity-time graph, displacement is the area under the graph. 6 A line of best fit may reduce measurement errors and allow us to find an algebraic equation to describe the motion. Set 3 - Interpreting velocity-time graphs 7 a) 0 b) 6.67 ms -2 c) 70 m 8 a) i) 2 ms -2 ii) 0 Page 7

8 iii) -2 ms -2 iv) 2 ms -2 b) i) 27 m ii) 36 m iii) 27 m c) 45 m d) 9 a) 1 ms-2 b) -3 ms -2 c) 0 d) -3 ms -2 e) 24 m f) 46.5 m g) 25.5 m 10 See graph below. The total distance travelled was 975 m. Page 8

9 11 a) 6 ms -1 b) 2.8 s c) Best estimation between 2.2 < t < 2.6 s d) 1.1 ms-2 e) Best estimation is about m Page 9

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