Kinematics in one dimension

This paragraph introduces the two branches of the science of moving objects: kinematics and dynamics. Kinematics deals with the concepts needed to describe motion, while dynamics focuses on the effects of forces on motion. Together, they form the branch of physics known as mechanics. The lecture primarily focuses on mechanics, discussing the position of an object in space, the introduction of a one-dimensional reference frame, and the concept of position vectors. It also explains how to use these vectors to define the position of a moving object at different times during its motion, with examples such as a car moving along a straight line and the definition of displacement.

This section delves deeper into the concepts of displacement and distance, emphasizing their differences and how they relate to the motion of objects. Displacement is defined as the straight-line distance between two positions and is a vector quantity, indicating direction as well as magnitude. Distance, on the other hand, is the total length of the path traveled and is a scalar quantity. The paragraph uses examples to illustrate how displacement and distance can differ, especially when the path of motion is not a straight line. It also introduces the concept of average speed, which is the distance traveled divided by the time taken, and explains that it is a scalar quantity without direction.

This part of the lecture focuses on the importance of signs in displacement calculations. The sign of a displacement vector indicates its direction relative to the chosen coordinate system. Positive displacement values indicate movement in the positive direction, while negative values indicate movement in the opposite direction. The paragraph provides examples of calculating displacement with proper sign considerations, highlighting the impact of the initial and final positions on the resulting displacement vector. It also introduces the concept of average velocity, which is a vector quantity that provides more information than average speed, including direction.

This paragraph discusses the graphical representation of average velocity, which is the slope of the curve representing position versus time on a graph. By selecting two points along the trajectory of motion and calculating the displacement and the time interval between these points, one can determine the average velocity. The lecture explains that the graphical meaning of average velocity is the slope of the curve between two points, and it provides an example of how to calculate average velocity for a jogger given the distance and time of the run.

This section presents example calculations of average velocity, using the scenario of a test driver attempting to set a world record for the fastest speed with a car. The driver makes two runs in opposite directions to account for wind effects, and the average velocity is calculated for each run, highlighting the significance of the minus sign in vector calculations. The paragraph emphasizes that while velocity as a physical quantity is always positive, the direction of motion is indicated by the sign of the velocity vector in the reference frame.

This paragraph introduces the concept of instantaneous velocity, which is the velocity of an object at a specific point in its trajectory. It is calculated as the limit of the average velocity as the time interval approaches zero, essentially the slope of the tangent to the trajectory at that point. The lecture notes that instantaneous velocity requires knowledge of calculus, which is not covered in this course. The paragraph then transitions to the topic of acceleration, which describes the rate of change of velocity over time. The definition and calculation of average acceleration are provided, along with examples of positive and negative acceleration, emphasizing the vector nature of acceleration and the importance of direction indicated by the sign of the result.

This section introduces the five kinematic variables essential for analyzing motion with constant acceleration: displacement, acceleration, final velocity, initial velocity, and time. The lecture presents the four kinematic equations that relate these variables, allowing the calculation of one quantity when the other three are known. These equations are crucial for solving problems involving the kinematics of motion. The paragraph also discusses the strategy for solving kinematics problems, including sketching the problem, identifying known and unknown variables, selecting the appropriate equation, and calculating the unknown quantity. The importance of considering the direction of motion when solving problems is reiterated.

This paragraph demonstrates the application of kinematic equations through examples involving a speed boat and an aircraft carrier. The examples show how to use the equations to calculate displacement and the length of the deck required for a jet to take off safely. The lecture emphasizes the importance of using the correct signs when substituting values into the equations and the need to consider the physical situation when interpreting the results, as some problems may have two possible solutions.

This section discusses freefall motion, which occurs when an object is released from rest and falls under the influence of gravity. The kinematic equations for freefall are presented in two different notations: one using the symbol 'a' for acceleration and another using 'G' for gravitational acceleration. The equations account for the constant acceleration due to gravity, which is directed vertically downward. The lecture provides an example of a stone falling from a tall building, illustrating how to use the equations to calculate the displacement and final velocity of the object after a given time of freefall.

The lecture concludes with a recap of the importance of understanding the definitions of kinematic quantities for describing the motion of objects. It emphasizes that the concepts learned in this lecture can be expanded to more than one dimension, which will be covered in the next lecture. The summary reinforces the significance of the kinematic equations and the need to accurately account for the direction of motion when solving problems involving the motion of objects.