Kinematics A Description of Motion

KINEMATICS: MOTION A DESCRIPTION OF MECHANICS Mechanics is a branch of physics that deals with the motion of objects and the forces that change. It also deals with the particles that are moving either with less velocity or they are at rest. It is also called Classical Mechanics or Newtonian Mechanics. Mechanics is of vital importance in describing motion of material bodies, such as planets, rockets, falling objects, and baseballs. Areas of Mechanics • • • Kinematics describes the quantitative description of motion such as the rate at which the particles are moving (velocity) and the rate at which their velocity is changing (acceleration). Dynamics deals with forces and their effect on motion. It also includes the study of the effect of torques in motion. Statics deals with the study of forces acting on bodies at rest. When in static equilibrium, the system is either at rest, or its center of mass at constant velocity. MOTION Motion is the displacement of an object in relation to objects that are considered to be stationary. Motion can also be defined as the continuous change of position with respect to a certain reference point. TYPES OF MOTION • • • Rectilinear/Translatory motion is the motion of a body along a straight line. Linear motion is the most basic of all motions. According to Newton's First law of Motion, objects that are not subjected to forces will continue to move uniformly in a straight line indefinitely. An example of linear motion is that of a ball thrown straight up and falling back straight down. Curvilinear/Rotational motion is the motion along a circular path. An example is a car negotiating a curve. Vibrational motion is a to and fro motion of a body. An example is a moving pendulum. LESSON 5: MOTION IN A STRAIGHT LINE SPEED AND VELOCITY Galileo Galilei, the founder of modern experimental science said that the motion of moving objects maybe described in terms of time rates of change. Therefore, the rates that describe motion are speed, velocity, and acceleration. Speed and velocity use the terms distance and displacement. Distance is a scalar quantity which represents the total path length. Displacement is the straight-line distance between the starting and end points. Speed is a scalar quantity which specifies magnitude of the rate of motion without reference to the direction of motion. It can also be defined as the distance traveled per unit of time. 𝒗= 𝒅 𝒕 In symbols, Speed can be expressed by the units cm/s, m/s, km/h, ft/s, mi/h, etc. Average speed is the total distance traveled divided by the total time to travel that distance. ave. speed = 𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑒𝑑 𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒 𝑡𝑜 𝑡𝑟𝑎𝑣𝑒𝑙 𝑡ℎ𝑎𝑡 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑑 =𝑣= 𝑡 Velocity is the total displacement covered in a given time interval. It can also be defined as a speed in a given direction. ACCELERATION Acceleration is a vector quantity which describes how velocity changes with time. Mathematically, acceleration is expressed as 𝒂= 𝒗𝒇 − 𝒗𝒊 𝒕𝒇 − 𝒕𝒊 Problem 2 During a race, a sprinter increases from 5.0 m/s to 7.5 m/s over a period of 1.25s. What is the sprinter's average acceleration during this period? Given: 𝑣𝑖 =5.0 m/s Where 𝑣𝑓 = final velocity 𝑣𝑖 = initial velocity 𝑣𝑓 = 7.5 m/s 𝑡𝑓 = final time 𝑡𝑖 = initial time t = 1.25 s When an object starts moving from rest, the equation becomes Find. Ave. acceleration Solution: 𝒗 𝒂= 𝒕 𝑎= 𝑎= Calculating acceleration involves dividing velocity by time or in terms of units, dividing meters per second [m/s] by second [s]. Dividing distance by time twice is the same as dividing distance by the square of time. Thus, the SI unit of acceleration is the meter per second squared. 𝒎 𝒎/𝒔 𝒎 𝟏 = = 𝒙 𝒔𝟐 𝒔 𝒔 𝒔 Acceleration can also be expressed in units such as m/s2, km/h2, km/h/s. A moving object is accelerating when (1) the velocity is changing (increasing or decreasing); (2) the direction is changing; and (3) both velocity and direction is changing. Acceleration can be positive or negative. Deceleration indicates negative acceleration. Problem 1 As a shuttle bus comes to a normal stop, it slows from 9.0m/s to 0.0m/s in 5.0s. Find the average acceleration of the bus. Given: initial velocity = 9.0 m/s, final velocity = 0.0, time = 5.0 s Find: ave. acceleration Solution: 𝑎= 𝑎= 𝑣𝑓 − 𝑣𝑖 𝑡 0 − 9.0 𝑚/𝑠 5𝑠 𝑎 = −1.8 𝑚/𝑠 2 𝑣𝑓 − 𝑣𝑖 𝑡 7.5 𝑚/𝑠 − 5.0 𝑚/𝑠 1.25 𝑠 𝑎= 2.5 𝑚/𝑠 1.25 𝑠 𝑎 = 2 𝑚/𝑠 2