H1.02. 2022 Kinematics Notes

CJC H1 PHYSICS LECTURE NOTES JC1 2022 2(1) 2 Kinematics Main concept(s) 1. Rectilinear Motion 2. Non-Linear Motion (including Projectile Motion) Learning Outcome(s) Candidates should be able to: (a) show an understanding of and use the terms distance, displacement, speed, velocity and acceleration. (b) use graphical methods to represent distance , displacement, speed, velocity and acceleration. (c) identify and use the physical quantities from the gradients of displacement -time graphs and areas and gradients of velocity-time graphs, including cases of non - uniform acceleration. (d) derive, from the definitions of velocity and acceleration, equations which represent uniformly accelerated motion in a straight line. (e) solve problems using equations which represent uniformly accelerated motion in a straight line, including the motion of bodies falling in a uniform gravitational field without air resistance. (f) describe qualitatively the motion of bodies falling in a uniform gravitational field with air resistance. (g) describe and explain motion due to a uniform velocity in one direction and a uniform acceleration in a perpendicular direction. ~ Introduction Today, we use electronic stopwatches, video recorders and other sophisticated instruments to analyse motion, but it has not always been so. Galileo, who in the early 1600s was the first scientist to study motion experimentally, used his pulse to measure time! Galileo made a useful distinction between the cause of motion and the description of motion. “Kinematics” is the modern term for the mathematical description of motion without regard to causes. The term comes from the Greek word kinema, meaning “movement ”. This chapter begins with visualising motion and developing the representations for describing the positio n, displacement, velocity and acceleration of moving objects in space as a function of time . We will begin our study of kinematics with motion in one dimension, followed by two dimensions. Essential Questions • How do we describe the motion of objects? • How can the motion of objects be represented, quantified and predicted? • How can we tell if an object is moving with a constant acceleration? • How would an object experiencing constant acceleration in one direction and constant velocity in a perpendicular direction move? • How would an object falling in a uniform gravitational field move?

CJC H1 PHYSICS LECTURE NOTES JC1 2022 2(2) 1. 2.1 RECTILINEAR MOTION Rectilinear motion means motion in a straight line. 2.1.1 Displacement vs Distance Example 1 Consider a car moving to the left. The positions of the car at various instan ces in time t are represented as dots in a straight line. This straight line serves as a reference to a coordinate axis, just like the x-axis. To make the discussion of displacement meaningful, ❖ A reference point must be defined. For example, o If t = 0 s is taken as the reference point, then at time t = 2 s, the displacement from that point is 20 m. o If t = 1 s is taken as the reference point, then at time t = 2 s, the displacement from that point is 10 m. ❖ Additionally, a positive direction must be defined. o If the positive direction is defined to be leftwards and t = 1 s is taken as the reference point , then at time t = 0 s, the displacement of the car from th e reference point is -10 m. The negative sign is a mathematical representation to say that it is in the opposite direction to the positive direction. Note that since displacement is a vector, both magnitude and direction are specified. Since distance is a scalar quantity while displacement is a vector quantity, the displacement of an object may or may not be equal in magnitude to the distance it travels. t = 0 s t = 1 s t = 2 s t = 3 s 0 m 10 m 20 m 30 m Displacement is the straight-line distance of an object or a point, in a specified direction, from some reference point. The specified direction is directed from the reference point to that object’s position or that point. Displacement is a vector quantity. Distance is the total length of the actual path t ravelled by a moving object , irrespective of the direction of motion. It is a scalar quantity.

CJC H1 PHYSICS LECTURE NOTES JC1 2022 2(3) Example 2 Suppose the car in Example 1 reversed direction after travelling 40 m and returned to its initial position at t = 10 s. Motion diagram: Distance moved in 10 s from t = 0 s is 80 m. But, Displacement moved in 10 s from t = 0 s is 0 m. 2.1.2 Speed and Velocity Definition: Speed is a scalar quantity. SI unit: metre per second, m s-1 In Example 2, The spacing between dots becomes smaller from t = 3 s to t = 5 s, indicating that the change in displacement per unit time decreases, hence speed decreases. The spacing between dots becomes wider from t = 5 s to t = 7 s, indicating that the change in displacement per unit time increases, hence speed increases. The lengths of the arrows in the motion diagram represents the speed. If the spacing is wider for adjacent dots, the higher the speed of the car. From t = 0 s to t = 3 s, the lengths of the arrows are the same. In addition, they are also the same as the lengths of the arrow between t = 7 s to t = 10 s. Therefore, the speed of the car within these timings is the same. However, travelling to the left is different from travelling to the right, thus, a vector representation of how fast the car is moving in a particular direction is required. t = 6 s t = 0 s t = 1 s t = 2 s t = 9 s t = 8 s t = 7 s 40 m 30 m 0 m 10 m 20 m t = 10 s t = 5 s t = 3 s t = 4 s t = 6 s t = 0 s t = 1 s t = 2 s t = 9 s t = 8 s t = 7 s 40 m 30 m 0 m 10 m 20 m t = 10 s t = 5 s t = 3 s t = 4 s Speed is the rate of change of distance with respect to time.

CJC H1 PHYSICS LECTURE NOTES JC1 2022 2(4) Definition: Velocity is a vector quantity. Magnitude of velocity equals speed. Therefore, if the car in Example 2 is moving at 10 m s -1 between t = 0 s to t = 3 s, then, it is travelling at -10 m s-1 between t = 7 s to t = 10 s. [Note that positive direction was defined earlier as leftwards.] Example 3 Car A is moving to the left at 10 m s-1 and car B is moving to the right at 10 m s-1. Car A and car B are said to have the same speed but different velocity because the direction of their velocities are different. Example 4 A bus travels 50 m due east and makes a U-turn back to travel a further distance of 30 m. The total time taken is 100 s. Determine its (i) average speed (ii) average velocity Car A, 10 m s-1 Car B, 10 m s -1 Velocity is the rate of change in displacement with respect to time. Note: Velocities of the two cars are represented by arrows. The length of the arrows represent the magnitude. Since the two car are travelling at 10 m s-1, the magnitude of the velocity vectors are the same. Directions of velocity: car A point towards the left and car B point towards the right. 1sm0.8 100 80 timetotal distance in change totalspeedAve (i) −= = = eastduesm0.2 100 20 timetotal ntdisplaceme in changevelAve (ii) 1−= = =

CJC H1 PHYSICS LECTURE NOTES JC1 2022 2(5) 2.1.3 Motion Diagram with Velocity Vectors Back to Example 2, Define reference point to be the initial position, and, direction to the right as positive. Average speed of the car between t = 1 s and t = 8 s is (50 m / 7 s) = 7.1 m s-1. Average velocity of the car in the same time interval is determined as follows: Displacement at 1 s, s1 = -10 m Displacement at 8 s, s2 = -20 m Change in displacement, ∆s = s2 – s1 = (-20) – (-10) = -10 m (i.e. 10 m to the left) Average velocity = -10 m / 7 s = -1.4 m s-1 (i.e. 1.4 m s-1 to the left) Average velocity of the car between t = 0 s and t = 10 s is