Graphical Analysis of Motion
Interprets and uses position-time, velocity-time, and acceleration-time graphs to describe motion.
What is Graphical Analysis of Motion?
A graph that plots the position of an object on the y-axis against time on the x-axis.
Key formula / rule: Velocity from x-t graph
Key points
- Interpret position-time, velocity-time, and acceleration-time graphs.
- Calculate velocity from the slope of a position-time graph.
- Calculate acceleration from the slope of a velocity-time graph.
- Determine displacement from the area under a velocity-time graph.
Common exam trap
Confusing the slope of x-t graph with velocity and the slope of v-t graph with acceleration.
Definitions
- Term
Position-time graph (x-t graph)
- Meaning
A graph that plots the position of an object on the y-axis against time on the x-axis.
- Term
Velocity-time graph (v-t graph)
- Meaning
A graph that plots the velocity of an object on the y-axis against time on the x-axis.
- Term
Acceleration-time graph (a-t graph)
- Meaning
A graph that plots the acceleration of an object on the y-axis against time on the x-axis.
- Term
Slope
- Meaning
The measure of the steepness of a line, calculated as the ratio of the vertical change to the horizontal change between any two points on the line.
Learning objectives
Interpret position-time, velocity-time, and acceleration-time graphs.
Calculate velocity from the slope of a position-time graph.
Calculate acceleration from the slope of a velocity-time graph.
Determine displacement from the area under a velocity-time graph.
Describe the type of motion represented by different graph shapes.
Formulae
- Name
Velocity from x-t graph
- Note
Represents the slope of the position-time graph between two points.
- Expression
v = Δx / Δt = (x₂ - x₁) / (t₂ - t₁)
- Name
Acceleration from v-t graph
- Note
Represents the slope of the velocity-time graph between two points.
- Expression
a = Δv / Δt = (v₂ - v₁) / (t₂ - t₁)
- Name
Displacement from v-t graph
- Note
Can be calculated by summing areas of rectangles, triangles, or trapezoids under the curve.
- Expression
Δx = Area under the v-t graph
- Name
Change in velocity from a-t graph
- Note
Represents the total change in velocity over a time interval.
- Expression
Δv = Area under the a-t graph
Prerequisites
Basic understanding of coordinate systems (x and y axes)
Concept of slope of a straight line
Understanding of displacement, velocity, and acceleration
Basic algebraic equations
Common mistakes
Confusing the slope of x-t graph with velocity and the slope of v-t graph with acceleration.
Incorrectly calculating displacement from the area under the v-t graph, especially with non-rectangular areas.
Assuming that a curved line on an x-t graph always means acceleration, without considering the rate of change of slope.
Misinterpreting the direction of motion from the sign of velocity or displacement.
Keywords
Position-time graph
Velocity-time graph
Acceleration-time graph
Slope
Area under curve
Displacement
Velocity
Acceleration
Uniform motion
Non-uniform motion
Kinematics
Practice preview
The acceleration-time graph of a particle is a horizontal line below the time axis. What does this imply?…
easy
Which of the following statements is INCORRECT regarding the motion represented by a position-time graph?…
medium
A particle is moving such that its position-time graph is a straight line with a positive slope. What does this indicate about the particle's motion?…
easy