MOTION

Motion

      Motion is apparent in widely ranging phenomena, from blood cells squeezing through capillaries to planets moving across the sky. Motion is the displacement of an object with respect to objects that are at rest. Historically, motion was one of the first phenomena to be studied carefully. Some progress was made in the understanding of motion in ancient times, particularly by the philosophers of classical Greece, but it was not until the Renaissance that the basic laws of motion were discovered. Many individuals made important contributions, but two stand above the rest : Galileo Galilei (1564 – 1642) and Isaac Newton (1642 – 1727). If Galileo’s predecessors had placed a greater value on experimentation, they might have made more progress than they did. Instead most natural philosophy was based on logical argument and the constraining influence of a particular school of thought. The transition that Galileo and others made from dogma to experimentation was not without pain; Galileo himself was forced by the Inquisition to recant his work and lived the last years of his life under a form of house arrest.

      The central ideas regarding motion developed by Galileo and Newton remained essentially intact until 1905, when Albert Einstein (1879 – 1955) published his paper on the theory of relativity. Even today, the classical theory of Galileo, Newton and others describes motion with extremely good precision as long as the object  being described moves slower than about 1% of the speed of light. The study of motion is kinematics, motion being the displacement of objects with respect to objects that are at rest. Kinematics comes from the Greek word kinema, meaning motion, the same root from which we get the word cinema. Kinematics describes the position and motion of objects in space as a function of time but does not consider the causes of motion.( It deals with motion without considering the forces causing the motion). The study of the causes of motion is dynamics which relates motion to the forces causing it and to the properties of the moving system.

      Kinematics provides the means for describing the motions of varied things as planets, golf balls, and subatomic particles. Because of its precision and generality, mathematics is the natural language for kinematics. To adequately describe motion, one must be able to say where something is located within a given reference frame. Reference frame is a physical entity, such as ground, a room or a moving car, to which we refer the position and motion of the objects.

      To say that space is three dimensional, it means that three numbers are needed to completely locate the position the position of an object. A system for assigning these 3 numbers, or coordinates, to the location of a point in a reference frame is called coordinate system. Because the coordinate system is a mathematical construction, you are free to choose the system that you want, orient it as you wish, and place its origin wherever you prefer.       

  TIME, DISPLACEMENT, VELOCITY AND ACCELERATION

            Time is measured in terms of change. If nothing changes, then it is impossible to tell that time has passed. All devices that measure time measure change; i.e., days are measured by the change in position of the sun in the sky, clocks measure elapsed time by the change in position of their hands.

            Displacement is the location of an object relative to a reference point. Displacement is specified by the distance from a reference point (magnitude) and the direction to get to the present location, it is a change in position in a specific direction. This implies that displacement is a vector quantity which has magnitude and direction. Distance has no given direction and has only magnitude, it is a change in position. It is a scalar quantity.

            Velocity and Speed. Speed is time rate of change of position while velocity is time rate of change of displacement. Velocity can also be describe as speed in a specific direction.

              ν =   Change in displacement  =    Δ S      

                           Change in time                  Δ t

                ν  is average velocity 


Uniform motion – a type of motion characterized by  constant or average speed.

            Equation of uniform motion                         

                                         S = vt  

                             

                                         v = S/t                      

                                          t = S/v  

                                   where :

                                              S = distance

                                              v =  constant or average speed

                                              t  =  time

Example 

1. A truck travels a distance of  90 km in 1.5 hours. Determine the average velocity. How many km does it go in 2.5 hours? How many minutes will it be able to travel 20 km?

                                       Given :

                                            S = 90 km

                                            t  = 1.5 hr

                                      Required :

                                           a) v

                                           b) S  in km when t = 2.5 hrs

                                           c) t  in seconds when  S = 20 km   

                                     Solution :

                                         a)  v = S/t

                                               v = 90km/1.5 hr

                                               v = 60 km/hr

                                        b)  S = vt = 60 km/hr( 2.5 hr)

                                             S  = 150 km

                                        c)  t = S/v  = [    20 km   ][  60 min  ]

                                                                 60 km/hr     1 hr

                                             t  =  20 min

  

    2.  Two cyclists starts from  common point in the opposite direction. Cyclist A moves to the east at 8 km/hr and Cyclist B towards the west. If cyclist B is 4 km/hr faster than cyclist A, in how many minutes will they be 24 km apart? What are their respective distance travelled during this period ? How far are they after one hour ?

   3.  A van starts from Midsayap with an average speed of 61 km/hr for Davao City. How many hours shall it reach Davao City? How far from Midsayap is the van after 75 minutes? How many hours shall it be able to  travel  106.75 km ?

   4.  A Mindanao Star bus leaves  the  Midsayap  terminal  at  6:00 AM  for  Davao  City with an average speed of 42 km/hr. At 6:45 a van leaves the same terminal for Davao City with an average speed of  60 km/hr. Can the van overtake the bus ? If so, where and when shall overtaking take place ?   

   5. A car has an average speed of 25 m/s. What is the distance travelled in 75 minutes? How many minutes shall it  travel a distance of 120 km?