Kinematics JPJC Notes

Kinematics Lecture Note 2023/JPJC/H2 Physics 1 JURONG PIONEER JUNIOR COLLEGE 9749 H2 PHYSICS/ 8867 H1 PHYSICS 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 repres ent 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 direction. Introduction The study of physics often begins with Newtonian Mechanics which investigates relationships between force and motion. The study of motion can be divided into two aspects: how objects move (kinematics) and why objects move in different ways (dynamics). Models and representations such as motion diagrams, graphs and equations are used to quantify, describe and predict motion. Motion in the real world is rather complex. The study of motion at this level is made simple with the use of assumptio ns. One valid assumption is to model the moving body as a point with no size where effects such as rotation or change of shape are not considered. It is also appropriate to ignore air resistance in solving most problems. Key Questions: 1. How do we describe the motion of objects? 2. How can the motion of objects be represented, quantified and predicted? 3. How can we tell if an object is moving with a constant acceleration? 4. For an object falling freely in a gravitational field, how would it move?

Kinematics Lecture Note 2023/JPJC/H2 Physics 2 1 Kinematics Quantities (a) Show an understanding of and use the terms distance, displacement, speed, velocity and acceleration. 1.1 Distance and Displacement Distance travelled (scalar) is the total length moved along the path of motion. Displacement (vector) is the linear distance in a specified direction from a reference point. Example 1 A man at point A travels 4.0 km due East to point B. He then travels a further 3.0 km due North to point C. Determine the total distance travelled and his displacement from the original position (point A). 1.2 Speed and Velocity Speed (scalar) is the rate of change of distance moved by an object. Velocity (vector) is defined as the rate of change of displacement. Instantaneous speed is the speed of a moving object at a particular instant. If an object travels along a path with varying speeds, we can always identify the smallest and largest speeds attained during its motion. The average speed lies between these two extremes. Normally when we mention about velocity, we are referring to instantaneous or constant velocity, unless otherwise stated. speed velocity instantaneous speed at a particular instant = small distance travelled short time taken = dx dt velocity at a particular instant = small displacement short time taken = dt ds average average speed between 2 instants = total distance travelled total time taken = x t   average velocity between 2 instants = displacement time taken = s t    Total distance travelled 4 0 3 0 7 0 km. . .   2 2 2 AC is the displacement 4 0 3 0 5 0 km 30 40 37 s s . . s. .tan .      The displacement from A is 5.0 km in a direction 37 North of East.

Kinematics Lecture Note 2023/JPJC/H2 Physics 3 Example 2 The man in Example 1 took 1 hour to move 4.0 km due East to point B, and another 1 hour to move 3.0 km due North to point C. Determine the man’s average speed and average velocity for the entire journey. Avg speed = total distance travelled total time taken Avg velocity = displacement time taken = 7.0 2 = 3.5 km h1 = 5.0 2 = 2.5 km h1 1.3 Acceleration Acceleration (vector) is defined as the rate of change of velocity.  Instantaneous acceleration, a = dt dv  Average acceleration , <a> = t v   where v = change in velocity = final velocity – initial velocity = vf – vi or = v – u Since velocity is a vector quantity, change in velocity v is also a vector with a magnitude and a direction. A change in velocity occurs when either the magnitude or the direction changes, or both the magnitude and direction change. Example 3 A particle has an initial horizontal velocity vi of 10 m s1 towards the right. A short time later, its velocity vf is 15 m s1 at an angle of 60 to the horizontal, as shown. Calculate the change in velocity that has taken place. fiv v v   = ()fivv (v)2 = 102 + 152 – 2(10)(15) cos 60 v = 13.2 m s1 10 13.2 sin sin60    = 41 The change in velocity is 13.2 m s1 at an angle of 41 to the left of the final velocity. The average velocity is 2.5 km h1 in a direction 37 North of East. 60o 10 m s-1 15 m s-1

Kinematics Lecture Note 2023/JPJC/H2 Physics 4 1.4 Using + and  to represent directions For 1-D (straight line) motion, directions of displacement, velocity and acceleration can be represented using ‘+’ and ‘ ’ signs. The figure below shows the usual sign convention to denote directions. displacement with respect to reference point + right above  left below velocity and acceleration + towards right upwards  towards left downwards Note that the sign convention can be reversed. It is valid as long as it is consistently applied within the same context. 1.5 Acceleration vs Deceleration Deceleration is a term used to describe an object slowing down (speed decreases). It is not the same as negative acceleration as the negative sign denotes direction only. The sign of the acceleration is not sufficient to provide information on whether the object is moving faster or slower. For example, if upwards is taken as positive, a ball then falls with an acceleration of 9.81 2m s . The negative sign denotes the downward direction of acceleration, hence the ball speeds up as it falls. To determine if an object speeds up or slows down, we need to look at both the velocity and acceleration at the same time.  When an object’s velocity and acceleration are in the same direction, the speed of the object increases with time.  When an object’s velocity and acceleration are in the opposite direction, the speed of the object decreases with time. The object is said to be undergoing deceleration. 1.6 Free fall An object is said to be in free fall if the only force act ing on it is the gravitational force of the Earth. The downward acceleration of a body undergoing free fall is known as acceleration of free fall, g, and has a constant value of 9.81 m s2. All free-falling objects have this acceleration, independent of their masses and direction of motion. For a falling object, true free fall only exists in a vacuum where there is no air resistance. physical quantity symbol definition nature SI base unit displacement s linear distance from a reference point, along a specified direction. vector m speed v rate of change of distance travelled. scalar 1m s velocity v rate of change of displacement. vector 1m s acceleration a rate of chang