Motion in One Dimension

Introduction

Motion in one dimension, also known as linear motion, describes the movement of objects along a straight line. This topic is foundational in physics, as it introduces the concepts of displacement, velocity, and acceleration, and provides the mathematical framework for analyzing motion under constant acceleration.

Velocity and Acceleration

Definitions and Equations

• Velocity is the rate of change of position with respect to time.

• Acceleration is the rate of change of velocity with respect to time.

Constant Acceleration

Graphical Representation

• When acceleration is constant, remains unchanged over time (horizontal line on a graph).

• Velocity () changes linearly with time under constant acceleration (straight, sloped line).

• Position () changes parabolically with time (curved line), as the slope of the position-time graph (velocity) changes linearly.

Equations for Constant Acceleration

These equations are derived from the definitions above and are essential for solving kinematics problems:

For vertical motion (often used in free fall problems):

Table: Constant Acceleration Equations

Free Fall

Characteristics of Free Fall

• An object in free fall experiences a constant downward acceleration due to gravity.

• The magnitude of gravitational acceleration is (use for estimation).

• Acceleration in the vertical direction:

• In the absence of air resistance, all objects fall with the same acceleration, regardless of their mass.

Example: Apollo 15 Feather and Hammer Experiment

This famous experiment demonstrated that, in the absence of air resistance, objects of different masses fall at the same rate.

Problem Solving in Kinematics

Worked Example

Scenario: A person stands on top of a building of height 80 m and throws a ball straight up with an initial speed of 20 m/s. The ball just misses the edge of the building on its way down. (Use for calculation.)

• a) Calculate the time to reach the highest point.

• b) Find the height of the highest point above the ground.

• c) Determine the velocity with which the ball hits the ground.

Steps for solving kinematics problems:

1. Complete diagram: Draw initial velocity, acceleration, axes, and label positions.

2. Write the starting equation.

3. Substitute given values into the equation.

4. Derive a symbolic answer.

5. Calculate the numerical answer, including units.

Summary: Litany for Kinematics Problems

• Draw a complete diagram, including velocity, acceleration, axes, and positions.

• Start with the appropriate kinematic equation.

• Replace generic variables with problem-specific values.

• Derive symbolic and numerical answers, always including units.

Additional info: These notes provide a structured approach to solving one-dimensional motion problems, emphasizing the importance of diagrams, equations, and careful substitution of values. The equations and methods outlined are foundational for all subsequent topics in kinematics and dynamics.