Motion in a Straight Line

Motion is all around us, from a ball rolling down a slope to a train leaving a station. This chapter studies the simplest kind, rectilinear motion, which takes place along a straight line, treating moving objects as point objects. It begins by choosing a reference point and axis to specify position, and distinguishes path length, which is a scalar, from displacement, which is a vector. You will learn about average velocity, average speed and instantaneous velocity, v = dx/dt. Acceleration is the rate of change of velocity, a = dv/dt. The chapter explains how position-time and velocity-time graphs represent motion: the slope of an x-t graph gives velocity, the slope of a v-t graph gives acceleration, and the area under a v-t graph gives displacement. For uniformly accelerated motion, you will derive the kinematic equations v = v0 + at, x = v0 t + (1/2)at^2 and v^2 = v0^2 + 2ax, and apply them to braking distance, free fall and reaction time.

Detailed Worksheet: Motion in a Straight Line Section A - Definitions (10 marks) 1. Distinguish between path length and displacement. (2 marks) 2. Define instantaneous velocity. (2 marks) 3. What does the slope of a velocity-time graph represent? (2 marks) 4. Can a body have zero velocity but non-zero acceleration? Give an example. (2 marks) 5. A car accelerates from rest at 2 m/s^2 for 10 s. Find its final velocity. (2 marks) Section B - Calculations and Applications (15 marks) 6. A ball is thrown vertically upwards at 20 m/s. Find the maximum height and the total time in the air. Take g = 10 m/s^2. (3 marks) 7. A car moving at 30 m/s brakes with a uniform deceleration of 5 m/s^2. Find the stopping distance and the time taken to stop. (3 marks) 8. A man walks 10 km at 30 km/h and returns along the same path at 20 km/h. Find his average speed and average velocity for the whole trip. (3 marks) 9. The position of a particle is x = 2t^2 + 3t metres. Find its velocity at t = 2 s and its acceleration. (3 marks) 10. Find the distance covered in the third second by a body falling freely from rest. Take g = 10 m/s^2. (3 marks) Section C - Diagrams (10 marks) 11. Draw position-time graphs for (i) a body at rest (ii) uniform motion (iii) uniformly accelerated motion. (4 marks) 12. Draw the velocity-time graph of a ball thrown vertically upwards until it returns to the thrower's hand. (3 marks) 13. A train accelerates uniformly from rest to 20 m/s in 10 s, moves at constant speed for 30 s, and then stops uniformly in 20 s. Draw its velocity-time graph. (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 ball is thrown vertically upwards at 20 m/s from the top of a building 25 m high. Find (i) the maximum height above the ground (ii) the time it takes to hit the ground. Take g = 10 m/s^2. (5 marks) 16. For the train in the graph question above, find the total distance covered and the average speed using the velocity-time graph. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Take g = 9.8 m/s^2 unless stated otherwise. Take the upward direction as positive for vertical motion.