Theme A — Space, Time and Motion
A.1.5 Motion Graphs — IB Physics HL Revision Notes & Topical Questions
5 min read 10 parts Lesson 7 of 63 1 quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Lesson summary
A.1.5 Motion Graphs — IB PHYSICS SL notes: Interpret and sketch displacement–time, velocity–time and acceleration–time graphs using gradients and areas.Three graphs — displacement–time, velocity–time and acceleration–time describe the same motion.Gradients and areas — each graph …
- y-intercept
- Horizontal line
- Straight sloping line
- Positive and negative slope
- Line returning to the time axis
- Instantaneous velocity
Section 1 of 10How the three graphs are linked
Three graphs
- Three graphs displacement–time, velocity–time and acceleration–time describe the same motion.
Gradients and areas
- Gradients and areas each graph is linked to the next by a gradient and to the previous by an area.
| Graph | Gradient | Area under line |
|---|---|---|
| Displacement–time (s–t) | Velocity | No meaning |
| Velocity–time (v–t) | Acceleration | Change in displacement |
| Acceleration–time (a–t) | No meaning | Change in velocity |
- y-intercept
- on each graph it gives the initial value of that quantity.
Section 2 of 10Displacement–time graphs
Displacement–time graphs
Horizontal line
- Horizontal line zero slope, the object is at rest.
Straight sloping line
- Straight sloping line constant velocity; a steeper line is a higher speed.
Curve
- Curve the velocity is changing, so the object is accelerating.
- A curve getting steeper means increasing velocity.
- A curve flattening means decreasing velocity.
Positive and negative slope
- Positive and negative slope motion in the positive or negative direction.
Line returning to the time axis
- Line returning to the time axis the object is back at its starting point.
Instantaneous velocity
- Instantaneous velocity the gradient of the tangent at that time.
Average velocity
- Average velocity the gradient of the chord between two points.
Section 3 of 10Velocity–time graphs
Velocity–time graphs
Horizontal line
- Horizontal line constant velocity.
- (rest only if v = 0)
Straight sloping line
- Straight sloping line uniform acceleration.
Curve
- Curve non-uniform acceleration.
- A curve getting flatter means the magnitude of acceleration is falling, as near terminal speed.
Positive and negative slope
- Positive and negative slope acceleration in the positive or negative direction.
Crossing the time axis
- Crossing the time axis the object stops instantaneously and reverses direction.
Section 4 of 10Areas under a velocity–time graph
Displacement
- Displacement the area between the line and the time axis.
- Areas above the axis count as positive and areas below as negative.
Distance travelled
- Distance travelled add the sizes of all the areas, ignoring sign.
Trapezium
- Trapezium area = ½ × width, which reproduces s = ½(u + v)t.
- (sum of parallel sides)
Section 5 of 10Acceleration–time graphs
Horizontal line
- Horizontal line constant acceleration; the rectangle area a × t is the change in velocity, v − u = at.
Line on the axis
- Line on the axis a = 0, constant velocity.
Varying line
- Varying line find the area by counting squares or splitting into simple shapes.
Initial velocity
- Initial velocity it cannot be read from the graph, because only the change in velocity is found.
Section 6 of 10Sketching a graph from a description
1Stage by stage
- Stage by stage split the motion into stages such as speeding up, constant speed and braking.
2Velocity–time shape
- Velocity–time shape a rising line, a horizontal line and a falling line form a trapezium whose area is the displacement.
3Displacement–time shape
- Displacement–time shape a curve getting steeper, a straight sloping line, then a curve flattening to a horizontal tangent.
4Acceleration–time shape
- Acceleration–time shape three horizontal steps: positive, zero and negative.
5Bouncing ball
- Bouncing ball its v–t graph is straight lines with gradient −g and a sudden jump in velocity at each bounce.
Section 7 of 10Reading graphs accurately
1Axes
- Axes read the axes and units, and check whether the quantity is distance or displacement.
2Gradient method
- Gradient method use a large triangle and as much of the graph as possible.
3Scattered data
- Scattered data draw a best-fit line; its gradient is a better estimate than any single pair of points.
4Uncertainty in a gradient
- Uncertainty in a gradient find it from the steepest and shallowest acceptable lines.
Section 8 of 10More from the specification
More from the specification
Axis scaling across motion range
- Axis scaling across motion range selecting appropriate coordinate scale intervals ensures displacement and velocity curves span the full graphical range clearly.
Vertical projectile motion
- Vertical projectile motion at maximum trajectory height, vertical velocity reaches zero before gravitational acceleration accelerates the projectile downwards.
Kinematic equations for uniform acceleration
- SUVAT equations calculate displacement, initial speed, final velocity, and acceleration when air resistance is negligible.
Terminal velocity of a skydiver
- Terminal velocity of a skydiver downward weight balances upward air resistance force, resulting in zero net force and constant final descent velocity.
Projectile Motion Components
- The motion of a launched projectile is analyzed by separating it into independent horizontal motion at constant velocity and vertical motion with constant gravitational acceleration (-9.81 m/s2.
Calculating Maximum Height
- Using kinematic equations of motion, the maximum vertical height is determined by setting the final vertical velocity component to zero (vy = 0).
- (v2 = u2 + 2as)What the symbols mean: v = final velocity · u = initial velocity (m s−1) · a = acceleration (m s−2) · s = displacement (m)
- (v2 = u2 + 2as)
Terminal Velocity and Air Resistance
- For a falling skydiver or accelerating cyclist, drag force from air resistance increases with speed until it equals driving or gravitational force,
- resulting in zero net force and terminal velocity.
Graphical Analysis of Freefall Motion
- A velocity-time graph for an object falling with air resistance displays an initially steep gradient (g) that progressively flattens to a horizontal asymptote as terminal speed is reached.
Fluid resistance
- Drag force from a fluid opposing motion.
Scalar quantity
- A quantity with magnitude only, such as potential
Projectile
- Object moving under gravity alone in two dimensions.
Resistance
- Opposition to current, R = V / I, in ohms (Ω).
Vector
- Quantity with magnitude and direction.
Maximum height
- The greatest height reached, where the vertical velocity is zero.
Projectile motion
- Two-dimensional motion with constant horizontal velocity and vertical acceleration g.
Kinematic equations
- Equations relating displacement, velocity, acceleration and time for constant acceleration.
Final velocity
- Velocity at the end, v.
Velocity-time graph
- A graph of velocity against time whose gradient is acceleration and area is displacement.
Section 9 of 10Key terms
| Term | Meaning |
|---|---|
| Gradient | Change in y divided by change in x on a graph |
| Tangent | Straight line touching a curve at one point; its gradient is the instantaneous rate |
| Area under graph | Product of the two axis quantities, summed over the interval |
| Displacement–time graph | Gradient gives velocity |
| Velocity–time graph | Gradient gives acceleration; area gives displacement |
| Best-fit line | Line that follows the trend of scattered data |
Section 10 of 10Exam technique
1
Reading the height of a displacement–time graph as speed — speed is the gradient.
2
Counting areas below the axis as positive when finding displacement — they are negative.
3
Calling a horizontal v–t line at rest — it is constant velocity, and rest only if v = 0.
4
Using a point-to-point gradient for an instantaneous value — use a tangent.
5
Letting a distance–time graph slope downwards — distance never decreases.
Marked practiceQuizzes for this lesson
Last updated:
Physics 0625 & 9702 SUVAT Mastery
Graph Interpretation
Constant Acceleration Equations (SUVAT) & Slopes
v = u + at | s = ut + ½at2 | v2 = u2 + 2as | s = ½(u + v)t
- Displacement-Time Graph: Gradient = Velocity (curve = accelerating).
- Velocity-Time Graph: Gradient = Acceleration; Area under curve = Distance travelled / Displacement.
- Free Fall in vacuum:
a = g ≈ 9.81 m/s2downwards (air resistance negligible).