Motion

This chapter describes motion, the change in the position of an object with time. You will distinguish distance, the total path length, from displacement, the shortest distance from the initial to the final position in a given direction, and see that displacement can be zero even when distance is not. You will study uniform and non-uniform motion, speed, average speed and velocity, and acceleration, the rate of change of velocity, measured in m/s^2, which may be positive or negative. You will learn to draw and read distance-time and velocity-time graphs and to find the distance travelled from the area under a velocity-time graph. You will derive the three equations of uniformly accelerated motion, v = u + at, s = ut + (1/2)at^2 and v^2 - u^2 = 2as, and use them to solve problems about vehicles, trains and falling objects. Finally, you will learn about uniform circular motion, in which an object moves at constant speed but its velocity changes continuously because its direction changes, with speed v = 2 pi r / t.

Detailed Worksheet: Motion Section A - Definitions (10 marks) 1. Distinguish between distance and displacement. Can displacement be zero when distance is not? Give an example. (2 marks) 2. Define uniform motion and non-uniform motion with one example each. (2 marks) 3. Distinguish between speed and velocity. (2 marks) 4. Define acceleration. What is meant by uniform and non-uniform acceleration? (2 marks) 5. What is uniform circular motion? Why is it called accelerated motion? (2 marks) Section B - Calculations and Applications (15 marks) 6. An athlete completes one round of a circular track of diameter 200 m in 40 s. What will be the distance covered and the displacement at the end of 2 minutes 20 seconds? (Take pi = 22/7.) (3 marks) 7. A car travels 30 km at a uniform speed of 40 km/h and the next 30 km at a uniform speed of 20 km/h. Find its average speed. (3 marks) 8. A bus decreases its speed from 80 km/h to 60 km/h in 5 s. Find the acceleration of the bus in m/s^2. (3 marks) 9. A train starting from a railway station attains a speed of 40 km/h in 10 minutes. Find its acceleration in m/s^2, correct to three decimal places. (3 marks) 10. A racing car has a uniform acceleration of 4 m/s^2. What distance will it cover in 10 s after start? What will its final velocity be? (3 marks) Section C - Diagrams (10 marks) 11. Draw distance-time graphs for (i) uniform motion (ii) non-uniform motion (iii) an object at rest. Explain what the slope of each shows. (4 marks) 12. Draw a velocity-time graph for a car that starts from rest, accelerates uniformly to 20 m/s in 10 s, moves at constant speed for 20 s and then stops uniformly in 10 s. Find the total distance from the graph. (3 marks) 13. Draw a diagram of an object moving in a circular path and show the direction of velocity at four points. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Derive the three equations of motion for uniformly accelerated motion using the velocity-time graph. (5 marks) 15. A train is travelling at 90 km/h. Brakes are applied so as to produce a uniform acceleration of -0.5 m/s^2. Find how far the train will go before it is brought to rest and the time taken. (5 marks) 16. An artificial satellite is moving in a circular orbit of radius 42250 km. Calculate its speed if it takes 24 hours to revolve around the Earth. (Take pi = 3.14.) Explain why its velocity changes even though its speed is constant. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Convert all quantities to SI units before using equations, and show every step.