LINEAR MOTION IN A STRAIGHT LINE: DISTANCE AND DISPLACEMENT
Understanding Basic Concepts and Real-World Applications
Presented by: Ma. Johanna B. Testa
OBJECTIVES
• Define linear motion in a straight line.
• Differentiate between distance and displacement.
• Analyze examples of linear motion in everyday and scientific contexts.
• Apply concepts to advanced real-life situations.
WHAT IS LINEAR MOTION?
• Motion along a straight line in one dimension.
• Can be uniform or non-uniform.
• Examples: Train moving on a straight track, arrow flying toward a target.
DISTANCE – CONCEPT
• Total length of the path traveled.
• Scalar quantity: Only magnitude, no direction.
• Always positive.
• SI Unit: Meter (m)
• Example: Walk 4 m east, then 3 m west → Total distance = 7 m
BASIC FORMULAS FOR DISTANCE
Uniform Motion (Constant Speed)
When an object moves at a constant speed in a straight line:
Distance = Speed × Time
Where:
Distance = total path covered (meters, m)
Speed = constant rate of motion (meters/second, m/s)
Time = duration of motion (seconds, s)
Uniformly Accelerated Motion (Variable Speed)
When motion has constant acceleration (like in free fall or car acceleration):
Where:
u = initial velocity (m/s)
a = acceleration (m/s²)
t = time (s)
Distance here equals displacement if in a straight line
From Final Velocity (No Time Known)
Where:
v = final velocity
u = initial velocity
a = acceleration
Formula for Distance in Free Fall:
Where:
d = distance fallen (in meters, m)
g = acceleration due to gravity (approximately 9.8m/s2 on Earth)
t = time in seconds (s)
DISPLACEMENT – CONCEPT
• Shortest straight-line distance from start to end.
• Vector quantity: Has magnitude and direction.
• Can be positive, negative, or zero.
• SI Unit: Meter (m)
• Example: 4 m east - 3 m west = 1 m east
DISTANCE VS DISPLACEMENT
Distance: Scalar, always positive, depends on path.
Displacement: Vector, can be zero/neg/pos, only start and end matter.
GRAPHICAL REPRESENTATION
Example: Go 5 m right → 2 m left
• Distance = 7 m
• Displacement = 3 m right
EQUATIONS OF MOTION (STRAIGHT LINE)
• s = ut + ½at²
• v = u + at
• v² = u² + 2as
(Where s = displacement, u = initial velocity, v = final velocity, a = acceleration, t = time)
APPLICATION 1 – AUTONOMOUS VEHICLES
• Use displacement to calculate routes.
• GPS & sensors track net displacement.
• Efficient pathing = fuel savings.
APPLICATION 2 – RUNWAY DESIGN IN AVIATION
• Aircraft motion follows displacement.
• Runway length uses distance; end-point analysis uses displacement.
APPLICATION 3 – ROBOTIC ARM IN MANUFACTURING
• Linear paths needed for precision.
• Displacement defines arm positioning.
• Example: PCB assembly.
APPLICATION 4 – SATELLITE DEPLOYMENT
• Initial launch follows straight-line displacement.
• Used to determine orbits and momentum.
APPLICATION 5 – BIOMEDICAL DEVICES (E.G., LINEAR ACTUATORS)
• Used in MRI beds, surgical robots.
• Precise displacement = patient safety.
SUMMARY
• Linear motion is foundational in physics and engineering.
• Distance = total path; Displacement = net position.
• Real-world applications highlight relevance.
REVIEW QUESTIONS
1. What is the difference between distance and displacement?
2. Can displacement be zero when distance is not?
3. Name an application where displacement is more important than distance.
REFERENCES
• Encyclopedia Britannica – Linear Motion
• Khan Academy: One-dimensional motion
• NASA JPL: Kinematics in Satellite Launch
• Oxford Academic Journals: Autonomous Vehicle Path Planning
• McGraw-Hill Physics for Scientists and Engineers
THANK YOU!