2.3 Time, Velocity, and Speed
3 min read•june 18, 2024
and speed are fundamental concepts in physics, describing how objects move through space and . These ideas form the basis for understanding more complex motion, allowing us to analyze everything from car trips to planetary orbits.
Grasping the difference between instantaneous and is crucial. This knowledge helps us interpret graphs, calculate displacements, and predict an object' future position. Understanding these concepts opens the door to more advanced topics in physics.
Velocity and Speed
Instantaneous vs average velocity
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- Velocity is a vector quantity that describes the rate of change of an object's position in a particular direction
- is the velocity at a specific instant or point in time
- Represents the slope of the tangent line to the position vs. time graph at that instant (speedometer reading)
- is the total divided by the total time interval
- , where is the change in position and is the change in time
- Represents the slope of the secant line connecting two points on the position vs. time graph (odometer reading)
- is the velocity at a specific instant or point in time
- is the change in position of an object, including both magnitude and direction (distance from starting point to ending point)
- Displacement is an example of a vector quantity
Velocity and speed calculations
- To calculate velocity, use the formula
- Velocity is positive when the object moves in the positive direction and negative when it moves in the negative direction (right is positive, left is negative)
- Speed is the magnitude of velocity, without considering direction
- To calculate speed, use the formula , where is the total distance traveled
- Speed is always positive or zero (cannot have negative speed)
- Speed is an example of a quantity
Position-time graphs for velocity
- The slope of a position vs. time graph represents the velocity of the object
- A straight line indicates constant velocity, with the slope equal to the velocity (45° line = 1 m/s)
- A curved line indicates changing velocity, with the at any point equal to the slope of the tangent line at that point (parabola)
- Horizontal lines on a position vs. time graph indicate zero velocity (object at rest)
- Positive slopes indicate motion in the positive direction, while negative slopes indicate motion in the negative direction (upward sloping line = positive velocity, downward sloping line = negative velocity)
Interpretation of velocity-time graphs
- The area under a velocity vs. time graph represents the displacement of the object
- Positive areas indicate displacement in the positive direction, while negative areas indicate displacement in the negative direction (area above x-axis = positive displacement, area below x-axis = negative displacement)
- The total displacement is the sum of the signed areas (positive and negative)
- The slope of a velocity vs. time graph represents the acceleration of the object
- A straight line indicates constant acceleration, with the slope equal to the acceleration (45° line = 1 m/s²)
- A curved line indicates changing acceleration, with the instantaneous acceleration at any point equal to the slope of the tangent line at that point (parabola)
- Horizontal lines on a velocity vs. time graph indicate constant velocity (no acceleration)
Motion and Reference
- is the branch of physics that describes the motion of objects without considering the forces causing the motion
- is the coordinate system from which an object's motion is observed
- describes how an object's motion appears from different frames of reference
- provide the foundation for understanding the relationship between forces and motion
Key Terms to Review (24)
Average speed: Average speed is the total distance traveled divided by the total time taken. It gives a scalar measure of how fast an object is moving overall along its path.
Average velocity: Average velocity is the total displacement divided by the total time taken for that displacement. It is a vector quantity that indicates both magnitude and direction.
Average Velocity: Average velocity is the ratio of the total displacement of an object to the total time taken to cover that displacement. It represents the overall speed of an object's motion over a given time interval, providing a measure of how fast an object moves on average during that period.
Displacement: Displacement is a vector quantity that refers to the change in position of an object. It has both magnitude and direction, indicating how far and in what direction the object has moved from its initial position.
Displacement: Displacement is the change in position of an object, measured from a reference point or origin. It describes the straight-line distance and direction an object has moved, without regard to the path taken.
Elapsed time: Elapsed time is the total time that has passed from the beginning of an event to its end. It is usually represented by the symbol $\Delta t$ and is measured in seconds in the SI unit system.
Frame of reference: A frame of reference is a system for specifying the precise location and time of events in space and can be thought of as a viewpoint from which motion is observed. Understanding this concept is crucial for analyzing motion because it allows us to compare the velocities and positions of different objects relative to one another, making sense of their movement in relation to a chosen point or background.
Instantaneous speed: Instantaneous speed is the speed of an object at a specific moment in time. It is the magnitude of the instantaneous velocity vector.
Instantaneous velocity: Instantaneous velocity is the velocity of an object at a specific moment in time. It is represented as the derivative of the position function with respect to time.
Instantaneous Velocity: Instantaneous velocity is the rate of change of an object's position at a specific instant in time. It represents the velocity of an object at a particular moment, as opposed to the average velocity over a period of time.
Kinematics: Kinematics is the branch of physics that studies the motion of objects without considering the forces that cause the motion. It focuses on parameters such as position, velocity, acceleration, and time, allowing us to describe how an object moves in space over time and understand various forms of motion.
Model: A model is a simplified representation of a physical system that helps to predict and understand the behavior of real-world phenomena. In physics, models can be mathematical equations, diagrams, or simulations.
Newton's Laws of Motion: Newton's Laws of Motion are a set of three fundamental principles that describe the relationship between an object and the forces acting upon it, governing the motion of objects and the interactions between them. These laws form the foundation of classical mechanics and are crucial in understanding various topics in introductory college physics.
Position-Time Graphs: A position-time graph is a visual representation of an object's position over time. It is a fundamental tool used to understand and analyze the motion of an object, particularly in the context of time, velocity, and speed.
Relative Motion: Relative motion refers to the motion of an object as observed from a particular frame of reference or point of view. It describes the relationship between the movement of an object and the movement of the observer or reference frame.
S: The symbol 's' is commonly used to represent distance or displacement in physics, particularly in equations of motion. It serves as a fundamental variable that quantifies how far an object travels from its initial position to its final position, regardless of the path taken. Understanding 's' is crucial for analyzing motion, as it is directly linked to concepts such as time, velocity, and the energy dynamics of systems.
Scalar: A scalar is a physical quantity that has only magnitude and no direction. Examples include mass, temperature, and electric potential.
Scalar: A scalar is a physical quantity that has only a magnitude, or numerical value, and no direction. Scalars are contrasted with vectors, which have both a magnitude and a direction. Scalars are commonly used in physics to describe various physical properties and quantities.
Time: Time is a fundamental quantity used to measure the duration of events and the intervals between them. It is usually measured in seconds (s) in the International System of Units (SI).
V: In physics, 'v' represents velocity, which is a vector quantity that indicates the rate of change of an object's position with respect to time, including its direction. Velocity is crucial in understanding motion, as it not only tells how fast an object is moving but also in which direction it is traveling. This concept extends beyond simple motion to fluid dynamics and electrical circuits, highlighting its versatility across different scientific fields.
Velocity: Velocity is a vector quantity that describes the rate of change in the position of an object over time. It includes both the speed of the object and the direction of its motion. Velocity is a crucial concept in understanding the motion of objects and the fundamental principles of physics.
Velocity-Time Graphs: A velocity-time graph is a graphical representation that shows how the velocity of an object changes over time. It is a fundamental tool in the study of kinematics, which is the branch of physics that deals with the motion of objects without considering the forces that cause the motion.
Δt: Δt represents the change in time, which is a crucial concept in understanding motion and physical processes. This term highlights the difference between two specific time points, enabling the calculation of rates such as speed and velocity. It also plays a vital role in analyzing thermal processes and energy transfer by showing how time intervals affect the behavior of materials and systems.
Δx: Δx, or delta x, represents the change in position or displacement of an object over a given time interval. It is a fundamental concept in the study of kinematics, which is the branch of physics that describes the motion of objects without considering the forces that cause the motion.