ASRJC Kinematics Notes

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 / 8867 2-1 Additional Notes Topic 2: Kinematics Content: • Rectilinear motion • Non-linear motion Learning Outcomes 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 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. (g) describe and explain motion due to a uniform velocity in one direction and a uniform acceleration in a perpendicular motion.

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 / 8867 2-2 Additional Notes Introduction Kinematics is the branch of mechanics which deals with the description of the motion of bodies. In this chapter, two types of motion will be covered, namely, • along a straight line (rectilinear motion), and • on a plane (non-rectilinear motion). A Terms of Reference for Kinematics A.1 Distance and Displacement • Distance is a scalar quantity while displacement is a vector quantity. • Distance refers to the length of the path travelled by a body regardless of the direction of motion. • Displacement is the distance of a body or a point, in a sp ecified direction, from reference point. Check Your Understanding 1 When displacement of a body is zero, the distance travelled by the body must be zero. (True / False) A.2 Speed and Velocity Speed is a scalar quantity while velocity is a vector quantity. Direction of the velocity is the same as the direction of the change in displacement. Definition: Speed is distance travelled divided by the time taken. Definition: Velocity is the rate of change of displacement. memorise memorise Distance Displacement Demonstrating Science Inquiry Skills The study of kinematics begins with the introduction of precise terminology and language for describing motion, to reduce ambiguity in expression and confusion in thought. Using multiple representations such as motion diagrams, graphs and equations, we can express motion of objects.

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 / 8867 2-3 Additional Notes A.3 Instantaneous Speed and Velocity versus Average Speed and Velocity Both average speed and average velocity are measured over a time interval t. However, the phase “how fast” more commonly refer to how fast a body is moving at a particular instant. Since a moving body often changes its speed during its motion, it is common to distinguish between the average quantity and instantaneous quantity. • Instantaneous speed is the speed at a particular point or a particular instant of time. Instantaneous speed = taken time small object theby travelled distance small = gradient of the distance-time graph at that instant • Instantaneous velocity v is the average velocity for a diminishing time interval t. v = rate of change of displacement ds dt = gradient of displacement-time graph at that instant Hence instantaneous velocity (or simply velocity) can be defined as the rate of change of displacement. Note: The instantaneous speed is always equals to the magnitude of the instantaneous velocity because distance and displacement become the same when they become infinitesimally small. • Average speed refers to the total distance travelled divided by the total time taken. • Average velocity refers to the total change in displacement of the body divided by the total time interval. = total change in displacementaverage velocity total time taken Some examples of speeds Speed / m s-1 Light 3.0 x 108 Electron around nucleus 2.2 x 106 Earth around Sun 3.0 x 104 Commercial jet airplane 2.5 x 102 (900 km h-1) Typical car speed 22 (80 km h-1) Walking speed 1.5 Snails 1.0 x 10-3 Instantaneous speed is akin to the speedometer reading at any given instance Average speed is akin to the average of all the speedometer readings during the course of the trip. = total distance travelledaverage speed total time taken

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 / 8867 2-4 Additional Notes Example 1 Based on the diagram below, describe the direction of velocities and displacements of the bodies A, B, C and D. (Take right as positive) Example 2 A person walks 50 m east, then 60 m west. Suppose this walk takes 40 s to complete. Determine the (a) total distance travelled, (b) total displacement, (c) average speed, (d) average velocity. Always try to assign the same convention for all vectors along the same line. Eg. the positive direction is the same for displacement and velocity. va vb vc vd A B C D Reference point West East 50 m 60 m The sign for displacement depends on the position of body with respect to reference point. The +/- sign of velocity indicates the direction of velocity which is also the direction of motion. Taking the direction pointing to the right as positive. (→+ve) A has _____ displacement (on the left of reference point), _____ velocity (moving in the _____ direction or to the _____) B has _____ displacement, _____ velocity (moving in the _____ direction or to the _____) C has _____ displacement, _____ velocity (moving in the _____ direction or to the _____) D has _____ displacement, _____ velocity (moving in the _____ direction or to the _____)

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 / 8867 2-5 Additional Notes A.4 Acceleration Acceleration is a vector quantity. S.I. unit is written as m s-2. • Average acceleration of any body is calculated using the equation: − = = v v ua tt where u = initial velocity v = final velocity after the time interval t In practice both velocity and acceleration can be taken to mean instantaneous velocity and instantaneous acceleration. • Instantaneous acceleration = dv dt = gradient of velocity-time graph at that instant • A body is accelerating if and only if it is changing its velocity. This can be shown in several ways: ➢ by change in magnitude only, i.e. the speed changes while the direction remains the same; ➢ by a change in direction only, e.g., a body moving with constant speed in a circular path; or ➢ by a change in magnitude and direction simultaneously. • If a body is changing its velocity - whether by a constant amount or a varying amount - then it is accelerating. ➢ Conversely, a body with a constant velocity is not accelerating. ➢ Constant acceleration means that the velocity is changing by a constant amount each second and there is no change in direction of acceleration. • Deceleration means that body is slowing down, regardless of direction of motion. Note: While acceleration can have a positive or negative value, deceleration can only have a positive value. Example 3 A car was travelling with an initial velocity u m s-1. After a time interval of t, it is moving at v m s-1. In the table below, calculate the acceleration for each time interval and