Unit 2: Constant Velocity Motion – Equations, Graphs, and Concepts

Unit 2: Constant Velocity Motion

Introduction to Constant Velocity Motion

Constant velocity motion describes the movement of objects that travel in a straight line at a steady speed. In this unit, we analyze how position changes over time and how to interpret and use position vs. time graphs.

• Constant Velocity: An object moves with constant velocity if its speed and direction remain unchanged over time.

• Position vs. Time Graph: A graphical representation where the position of an object is plotted on the y-axis and time on the x-axis.

• Origin: The reference point (usually at position zero) from which all positions are measured.

Position vs. Time Graphs

Position vs. time graphs are essential tools for visualizing and analyzing motion. The slope of the graph provides information about the object's velocity.

• Y-Intercept: The point where the graph crosses the y-axis represents the object's initial position at time zero.

• Slope: The slope of the position vs. time graph indicates the velocity of the object.

• Constant Slope: A straight line (constant slope) means the object moves at a constant velocity.

Key Formula

• Velocity from Slope:

$v = \frac{\Delta x}{\Delta t}$

• Where $v$ is velocity, $\Delta x$ is the change in position, and $\Delta t$ is the change in time.

Key Terms and Definitions

• Position ($x$): The location of an object relative to the origin.

• Displacement ($\Delta x$): The change in position of an object.

• Time Interval ($\Delta t$): The difference between two time measurements.

• Initial Position ($x_0$): The position of the object at the start of observation (at $t=0$).

• Final Position ($x$): The position of the object at a later time.

Equations for Constant Velocity Motion

• Position as a Function of Time:

$x = x_0 + v t$

• Where $x$ is the position at time $t$, $x_0$ is the initial position, and $v$ is the constant velocity.

• Displacement Equation:

$\Delta x = v \Delta t$

• Where $\Delta x$ is the displacement, $v$ is velocity, and $\Delta t$ is the time interval.

Examples and Applications

• Example 1: If a car starts at $x_0 = 5$ m and moves at a constant velocity of $2$m/s, its position after $4$ seconds is:

$x = 5\ \text{m} + (2\ \text{m/s})(4\ \text{s}) = 13\ \text{m}$

• Example 2: On a position vs. time graph, a straight line with a positive slope indicates motion in the positive direction; a negative slope indicates motion in the negative direction.

Interpreting Graphs

• Positive Slope: Object moves away from the origin.

• Negative Slope: Object moves toward the origin.

• Zero Slope: Object remains stationary (no change in position).

Summary Table: Key Quantities in Constant Velocity Motion

Quantity	Symbol	Unit	Equation
Position	$x$	meters (m)	$x = x_0 + v t$
Displacement	$\Delta x$	meters (m)	$\Delta x = v \Delta t$
Velocity	$v$	meters/second (m/s)	$v = \frac{\Delta x}{\Delta t}$
Time Interval	$\Delta t$	seconds (s)	$\Delta t = t_{final} - t_{initial}$

Additional info: Some content and equations have been inferred and expanded for clarity and completeness, based on standard physics curriculum for constant velocity motion.