Physics graph skills

Read scales, plot a point and use gradients and intercepts to interpret Physics graphs.

Practise

Calculate a gradient

Calculate the gradient using A and B, in m s⁻¹. It gives the object's velocity. Give your answer to 3 significant figures.

Read the axes and units. The values are also available in the table below.

Larger graph

Graph values

Coordinates
Point	Time / s	Displacement / m
A	10	4
B	30	8

Treat the displayed values as exact unless an uncertainty is stated.

Hint

Gradient = (vertical change) / (horizontal change). Use the same order for both subtractions; a falling line has a negative gradient.

Worked solution

A = (10 s, 4 m); B = (30 s, 8 m).
Gradient = (8 − 4) / (30 − 10) = 0.2 m s⁻¹.
Answer: 0.200 m s⁻¹ (3 significant figures).

Another question

Question type: Mixed practice

Report a problem

Calculate a graph gradient from two points

A potential-difference–current line passes through (0.10 A, 1.5 V) and (0.50 A, 7.5 V). Gradient = (7.5 − 1.5)/(0.50 − 0.10) = 15 V A⁻¹ = 15 Ω. Choose separated points on the fitted line; they need not be measured data points.

Read which quantity is on each axis. If current is vertical and potential difference horizontal, the gradient is conductance, 1/R. Dividing one coordinate by the other gives the gradient only when the relevant straight line passes through the origin.

Find uncertainty in a gradient

Read the scale before calculating

Count the small divisions between two labelled values. If 10 divisions span 2 seconds, each division is 0.2 s. Check whether the scale starts at zero.

Gradient and intercept

For a straight line, gradient = Δy / Δx. Use two well-separated points on the line and subtract in the same order. A falling line has a negative gradient. Use changes in the coordinates; y / x only gives the gradient when the line passes through the origin.

The vertical intercept is the value of y when x = 0. On a displacement–time graph it gives initial displacement, while the gradient gives velocity in m s⁻¹.

Best-fit lines

Follow the overall trend and balance points above and below the line. A best-fit line need not pass through a data point. The readings here are synthetic practice data; the exercise asks you to choose between three candidate lines.

Use the axes to interpret the gradient

For V against I, the gradient is V / I = R, in Ω. Reversing the axes gives 1 / R. For extension x against force F, x = F / k: the gradient is 1 / k. Convert extension to metres before finding k in N m⁻¹.

What this practice includes

Linear scales, plotting one point, signed gradients, intercepts, choosing a straight best-fit line, axes and two physical interpretations. Displayed values are treated as exact for practice. Numerical answers use 3 significant figures; plotting coordinates must match the stated values exactly.

Curve fitting, tangents, areas, logarithmic axes and gradient uncertainty are not included yet.

A-level relevance

AQA 7408: MS 3.2–3.5 (partial); AQA 7408: 3.4.1.3, 3.4.2.1 (selected); OCR A H556: 1.1.3(d)(i–ii), 3.1.1(c), 3.4.1(b–d) (partial). Tasks cover the selected skills listed above.

AQA specification · AQA mechanics and materials specification · OCR A specification