Physics • Year 11 • Module 2 • Lesson 5
Acceleration and Graphical Analysis
Lock in the core vocabulary and graph-reading rules for v–t graphs and F vs a graphs before tackling harder questions.
1. Term–definition match
The definitions below are shuffled. In the right-hand column write the matching term from this list: gradient, line of best fit, uniform acceleration, F vs a graph, velocity-time graph, acceleration, direct proportionality, Newton’s Second Law, rise/run, area under graph. 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | The slope of a line on a graph; calculated as rise divided by run between two points. | |
| 1.2 | A straight or curved line drawn through a scatter of data points to represent the overall trend, minimising deviations. | |
| 1.3 | A constant rate of change of velocity; produces a straight line on a velocity-time graph. | |
| 1.4 | A graph of net force (y-axis) against acceleration (x-axis); the gradient equals the mass of the object. | |
| 1.5 | A graph with velocity on the y-axis and time on the x-axis; the gradient gives acceleration and the area gives displacement. | |
| 1.6 | The rate of change of velocity; a vector quantity measured in m s². | |
| 1.7 | A relationship where doubling one variable exactly doubles the other; shown by a straight line through the origin on a graph. | |
| 1.8 | The law stating that the net force on an object equals its mass multiplied by its acceleration: Fnet = ma. | |
| 1.9 | The method for calculating gradient: change in y divided by change in x using points on the line of best fit. | |
| 1.10 | The region between a velocity-time graph line and the time axis; numerically equal to displacement in metres. |
2. True or false — with correction
Circle T or F for each statement. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)
2.1 The gradient of a velocity-time graph equals the displacement of the object. T / F
2.2 On an F vs a graph, the gradient equals the mass of the object because F = ma has the form y = mx. T / F
2.3 A straight line through the origin on an F vs a graph confirms that net force is inversely proportional to acceleration at constant mass. T / F
2.4 To find the gradient of a graph you should always use two widely-spaced points ON the line of best fit, not data points. T / F
2.5 A horizontal line on a velocity-time graph means the object has zero velocity. T / F
2.6 The units of the gradient of an F vs a graph are kg, because N ÷ (m s−2) = kg. T / F
3. Fill-in-the-blank paragraph
Use the word bank to complete the passage. Each word is used once. 8 marks (1 per blank)
Word bank:
acceleration · area · constant · direct proportionality · gradient · mass · origin · velocity
On a velocity-time graph, the ___________ of the line equals the acceleration, while the ___________ under the line equals the displacement. When a straight line passes through the ___________ on an F vs a graph, it indicates ___________ between net force and acceleration at ___________ mass. The gradient of this line equals the ___________ of the object, with units of kg. During uniform acceleration, the ___________ increases at a ___________ rate, producing a straight line on the v–t graph.
4. Function recall
Answer each question in 1–2 sentences using precise terms from the lesson. 8 marks (2 each)
4.1 What physical quantity does the gradient of a v–t graph represent, and how is it calculated?
4.2 Why does the gradient of an F vs a graph give the mass of the object? Reference the form of Newton’s Second Law.
4.3 What does the area under a velocity-time graph represent, and what are its units?
4.4 Why must the gradient of a graph be calculated using points on the line of best fit rather than directly from data points in the table?
5. Build a concept map
Draw labelled arrows between the six terms below to show how they connect. Each arrow must carry a linking phrase (e.g. “equals”, “is the gradient of”, “confirms”). Aim for at least 6 labelled arrows. 6 marks (1 per valid labelled arrow)
Supplied terms: F vs a graph · mass · gradient · Newton’s Second Law · line of best fit · direct proportionality.
6. Label the v–t graph features
The diagram below shows a velocity-time graph for an object undergoing uniform acceleration. Write the correct label for each box A–E. 5 marks (1 each)
| Box | What does it represent / label it |
|---|---|
| A | |
| B | |
| C | |
| D | |
| E |
Q1 — Term–definition match
1.1 gradient • 1.2 line of best fit • 1.3 uniform acceleration • 1.4 F vs a graph • 1.5 velocity-time graph • 1.6 acceleration • 1.7 direct proportionality • 1.8 Newton’s Second Law • 1.9 rise/run • 1.10 area under graph.
Q2 — True / false with correction
2.1 False. The gradient of a v–t graph equals acceleration (Δv/Δt). The area under a v–t graph equals displacement. These are the two most common mix-ups in this topic.
2.2 True. Fnet = ma can be written as F = m × a; comparing with y = mx, the gradient = m (mass). The y-intercept is zero (through the origin) when there is direct proportionality.
2.3 False. A straight line through the origin confirms direct proportionality (F ∝ a), not inverse proportionality. Inverse proportionality would produce a curved hyperbola.
2.4 True. Using data points introduces experimental error directly into the gradient calculation. The line of best fit averages out random errors, giving a more reliable gradient.
2.5 False. A horizontal line on a v–t graph means the velocity is constant (but not necessarily zero). The acceleration is zero. Only a line on the x-axis (v = 0, horizontal) means the object is stationary.
2.6 True. Units check: N ÷ (m s−2) = (kg m s−2) ÷ (m s−2) = kg. This unit check is required in NESA responses.
Q3 — Cloze paragraph
In order: gradient / area / origin / direct proportionality / constant / mass / velocity / constant.
Q4.1 — Gradient of v–t graph
The gradient represents acceleration (m s−2), calculated as Δv / Δt — the change in velocity divided by the change in time. For uniform acceleration this is constant, giving a straight line.
Q4.2 — Why gradient = mass on F vs a graph
Newton’s Second Law Fnet = ma can be rearranged to F = m × a. This has the form y = mx, where F is y, a is x, and the gradient m is mass. Therefore the gradient of an F vs a graph equals the mass of the object, with units of kg.
Q4.3 — Area under v–t graph
The area under a v–t graph represents displacement in metres (m). It is calculated as the area of the geometric shape formed between the line and the time axis (triangle or trapezoid for uniform acceleration).
Q4.4 — Line of best fit vs data points
Data points contain random experimental error (e.g. measurement uncertainty in timing). Using two specific data points to calculate gradient imports those errors directly. The line of best fit averages out all the errors across all data points, giving a more reliable and representative gradient.
Q5 — Sample concept map
Correct maps should include arrows such as:
- F vs a graph — gradient equals → mass
- gradient — calculated from → line of best fit
- mass — is derived from → Newton’s Second Law
- F vs a graph — straight line through origin confirms → direct proportionality
- direct proportionality — is stated in → Newton’s Second Law
- Newton’s Second Law — is the basis for → F vs a graph
Award 1 mark per valid labelled arrow (minimum 6 marked).
Q6 — v–t graph labels
A: The straight line — represents uniform (constant) acceleration. B: Velocity, v (m s−1) — the y-axis quantity. C: Time, t (s) — the x-axis quantity. D: Shaded area under the line — represents displacement (m). E: Rise/run construction (gradient triangle) — used to calculate acceleration from the line of best fit.