02 Kinematics Lecture Notes 2023

Hwa Chong Institution (College) H2 Physics C1 2023 1 Chapter 2 Kinematics Mike Powell flying through the air during the long jump finals at the 1992 Olympic Games in Barcelona, Spain. He holds the long jump world record of 8.95 m at the 1991 World Championships in Athletics (Tokyo). (Credits to pinterest.com) “The most important factor for the distance travelled by an object is its velocity at takeoff - both the speed and angle. Elite jumpers usually leave the ground at an angle of twenty degrees or less; therefore, it is more beneficial for a jumper to focus on the speed component of the jump. The greater the speed at takeoff, the longer the trajectory of the centre of mass will be. The importance of a takeoff speed is a factor in the success of sprinters in this event.” (http://en.wikipedia.org/wiki/Long_jump)

Hwa Chong Institution (College) H2 Physics C1 2023 2 TOPIC 2: KINEMATICS H2 Physics Syllabus 9749 Kinematics Learning Outcomes Students should be able to: Rectilinear motion (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 under 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. Projectile motion (g) describe and explain motion due to a uniform velocity in one direction and a uniform acceleration in a perpendicular direction. Playlist of lecture examples: https://youtube.com/playlist?list=PL_b5cjrUKDlZwgJjDB24gnT-yvQpEuV3c

Hwa Chong Institution (College) H2 Physics C1 2023 3 Table of Contents 2.0 INTRODUCTION ................................ ................................ ................................ .............................. 5 2.1 TERMINOLOGY ................................ ................................ ................................ ............................... 5 2.1.1 Distance vs. Displacement ................................ ................................ ................................ ................ 5 2.1.2 Speed vs. Velocity ................................ ................................ ................................ ............................ 5 2.1.3 Acceleration ................................ ................................ ................................ ................................ ...... 7 2.2 DESCRIBING RECTILINEAR MOTION USING DIAGRAMS ................................ ............................ 9 2.2.1 Ticker tape diagrams................................ ................................ ................................ ......................... 9 2.2.2 Vector diagrams ................................ ................................ ................................ .............................. 10 2.2.3 Recording motion using stroboscope ................................ ................................ .............................. 10 2.3 DESCRIBING RECTILINEAR MOTION USING GRAPHS ................................ .............................. 11 2.3.1 Displacement vs. Time Graph (s-t graph) ................................ ................................ ........................ 11 2.3.3 Summary of relations among s-t, v-t and a-t graphs ................................ ................................ ........ 12 2.4 DESCRIBING RECTILINEAR MOTION USING EQUATIONS (FOR UNIFORM ACCELERATION) 14 2.4.1 Derivation of the Equations of Motion (for uniform acceleration) ................................ ..................... 14 2.5 FREE-FALLING BODIES ................................ ................................ ................................ ................ 16 2.6 VISCOUS DRAG FORCE ................................ ................................ ................................ ............... 17 2.7 NON FREE-FALLING BODIES ................................ ................................ ................................ ....... 18 2.7.1 Velocity-time graph of object falling through air ................................ ................................ ............... 18 2.7.2 Terminal Velocity ................................ ................................ ................................ ............................ 20 2.8.1 Projectile Motion ................................ ................................ ................................ ............................. 22 2.8.2 Projectile Motion: General Launch Angle ................................ ................................ ........................ 24 2.8.3 2D Motion with Air Resistance ................................ ................................ ................................ ........ 30 FURTHER READINGS AND REFERENCES ................................ ................................ ............................. 32 Appendix I : Understanding the Calculus Notations ................................ ................................ ................... 32 TUTORIAL 2A KINEMATICS - 1D MOTION ................................ ................................ ............................... 35 Self-Review Questions ................................ ................................ ................................ ............................... 35

Hwa Chong Institution (College) H2 Physics C1 2023 4 Discussion Questions ................................ ................................ ................................ ................................ . 38 TUTORIAL 2B KINEMATICS - 2D MOTION ................................ ................................ ............................... 45 Self-Review Questions ................................ ................................ ................................ ............................... 45 Discussion Questions ................................ ................................ ................................ ................................ . 46

Hwa Chong Institution (College) H2 Physics C1 2023 5 2.0 Introduction Kinematics (from Greek κινεῖν, kinein, to move) is the branch of mechanics that describes the motion of objects without consideration of the causes leading to the motion. The study of why objects move falls under the branch of Dynamics. The first part of this chapter deals with one-dimensional motion of moving bodies in rectilinear motion. 2.1 Terminology 2.1.1 Distance vs. Displacement Distance, x Distance is the total length travelled by a moving object irrespective of the direction of motion. Displacement, s The displacement of an object from a reference point O is the linear distance and direction of the object from O. The linear distance refers to the shortest distance from the initial to the final position of an object moved from one place to another. Note that distance is a scalar quantity whereas displacement is a vector1 quantity. For illustration, in the diagram below, an object travels from point O to point P along the path represented by the solid line. The d istance travelled is represented by the length of the s olid line. The displacement is represented by the length and direction of the dashed line. 2.1.2 Speed vs. Velocity Speed, v The speed of an object is defined as the rate of change of distance travelled by an object with respect to time. Ve