Intro to Phys Sci I Mechanics Heat Instructor Carlos Perez Motion with Constant Velocity We will start the study of mechanics and moving objects with the simplest case a physical system moving with constant velocity There are two important features of this model the use of linear functions and equations to describe it and the fact that we can reduce the situation to one dimension only Later on our knowledge of this topic will also be essential to understand Newton s rst law of motion and to analyze what happens when velocity is not constant 1 Analysis Models Last week we discussed the importance of making models A particularly important model used in the solution to physics problems is an analysis model An analysis model is a common situation that occurs time and again when solving physics problems Because it represents a common situation it also represents a common type of problem that we have solved before When you identify an analysis model in a new problem the solution to the new problem can be modeled after that of the previously solved problem Analysis models help us to recognize those common situations and guide us toward a solution to the problem The form that an analysis model takes is a description of either 1 the behavior of some physical entity or 2 the interaction between that entity and the environment When you encounter a new problem you should identify the fundamental details of the problem and attempt to recognize which of the situations you have already seen that might be used as a model for the new problem For example suppose an automobile is moving along a straight freeway at a constant speed Is it important that it is an automobile Is it important that it is a freeway If the answers to both questions are no but the car moves in a straight line at constant speed we model the automobile as a particle under constant velocity which we will discuss in this section Once the problem has been modeled it is no longer about an automobile It is about a particle undergoing a certain type of motion a motion that we have studied before This method is somewhat similar to the common practice in the legal profession of nding legal precedents If a previously resolved case can be found that is very similar legally to the current one it is used as a model and an argument is made in court to link them logically The nding in the previous case can then be used to sway the nding in the current case We will do something similar in physics For a given problem we search for a physics precedent a model with which we are already familiar and that can be applied to the current problem When solving a problem you should avoid browsing through the notes looking for an equation that contains the unknown variable that is requested in the problem In many cases the equation you nd may have nothing to do with the problem you are attempting to solve It is much better to take this rst step Identify the analysis model that is appropriate for the problem To do so think carefully about what is going on in the problem and match it to a situation you have seen before Once the analysis model is identi ed there are a small number of equations from which to choose that are appropriate for that model sometimes only one equation Therefore the model tells you which equation s to use for the mathematical representation 2 Constant Velocity What happens when the instantaneous velocity of a system is the same as its average velocity We will give a quantitative answer to this question at the end of this unit For now it s enough to think of it qualitatively Remember that the average velocity gives a general description of a system s motion It is a quantity that describes how a system moved from point A to point B as though it had always moved at the same speed in the same direction i e at the same velocity throughout We know from experience and the examples discussed in class that 1 the actual physical situation can look di erent a system could be moving at di erent velocities during di erent stages of its motion Just think of the Getting to Painter Hall activities done in class to realize this When the instantaneous velocity is the same as its average velocity it means that the physical system is actually moving at the same rate in the same direction the whole time Since both the speed magnitude of velocity and the direction of motion do not change during the whole trip we can say that the system s velocity is constant The velocity vector is the same throughout the motion Let us analyze this further 2 1 Constant Speed Constant speed means constant magnitude of the velocity vector In other words v cid 126 v remains the same Example Let s imagine you record the following readings from the speedometer of your car Time seconds Speed m s 1 2 3 4 5 6 0 6 0 6 0 6 0 6 0 Since the speed of your vehicle doesn t change over time we can say that it is constant 2 2 Constant Direction of Motion In simple words constant direction of motion means moving in a straight line The system s path doesn t curve no turns no change of direction We can imagine that the arrow representing the velocity vector always points in the same direction Any change in the direction the system is moving means that its velocity changes Figure 1 The direction of motion of this car is changing that is why it moves in a circle The car may be moving at a constant speed but its direction of motion is not constant Thus its velocity is not constant Figure 2 The direction of motion of this car is constant that is why it moves in a straight line If the car is also moving at a constant speed we know that its velocity is constant 2 Example Imagine you are able to measure the direction of motion of your car as you drive it You already de ned a frame of reference so you know what you re measuring angles with respect to If your measurements look like this Time seconds Direction of motion degrees 1 2 3 4 5 77 77 77 77 77 then you can be certain that you are traveling in a constant direction Physically this looks like moving in a straight line 2 3 Magnitude and Direction of Constant Velocity Now we know that in order to have a constant velocity we need both constant speed and constant direciton of motion If either or both of these numbers change at some value of time then the velocity is not constant For instance the following case represents constant velocity Time seconds Speed m s Direction of motion degrees Both speed and direction of motion remain constant over