Everyone quotes $g = 9.8\ \text{m s}^{-2}$, but how would you actually measure it in a school lab? In this practical you drop objects, record their motion, and pull $g$ straight out of a graph's gradient, twice, by two different methods. Then you do the most important scientific step of all: compare the two values and judge how accurate and reliable your experiment really was.
You want to measure how fast a dropped object speeds up, but it falls too quickly to time by hand.
Before reading: what could you measure instead of $g$ directly, then turn into $g$ using a graph? Write one idea.
Drop an object, plot $s$ against $t^2$, and read $g$ off the gradient
If you release an object from rest and record how far it has fallen at several times, plotting distance against time-squared gives a straight line whose gradient hands you $g$.
From $s = ut + \tfrac{1}{2}at^2$ with $u = 0$ and $a = g$, we get $s = \tfrac{1}{2}g\,t^2$. Plotting $s$ (vertical) against $t^2$ (horizontal) is a straight line through the origin with gradient $\tfrac{1}{2}g$, so $g = 2 \times \text{gradient}$. The timing can come from a ticker-timer, a light gate, or video frame analysis.
Method 1: drop an object from rest and measure $s$ at several times. Since $s = \tfrac{1}{2}g\,t^2$, a graph of $s$ versus $t^2$ is a straight line with gradient $\tfrac{1}{2}g$, so $g = 2 \times \text{gradient}$.
Pause, copy the highlighted method into your book before moving on.
Did you get this? In a graph of $s$ versus $t^2$ for a dropped object, the gradient is $4.9\ \text{m s}^{-2}$. What is $g$?
Plot velocity against time and the gradient is $g$ directly
We just saw the $s$-vs-$t^2$ method. That raises a question: is there a graph whose gradient gives $g$ straight away, without the factor of two? This card answers it → a velocity–time graph, whose slope is the acceleration itself.
If instead you measure the falling object's velocity at several instants, a velocity–time graph is a straight line whose gradient is the acceleration, and that acceleration is $g$.
Using a ticker-timer or light gates, find the velocity at successive instants and plot velocity (vertical) against time (horizontal). The gradient is $a = g$ directly.
A falling mass passes light gates giving velocities of $2.0\ \text{m s}^{-1}$ at $t = 0.20\ \text{s}$ and $6.9\ \text{m s}^{-1}$ at $t = 0.70\ \text{s}$. Find $g$ from the v–t gradient.
Method 2: measure the falling object's velocity at several instants and plot velocity against time. The gradient of the straight line is the acceleration, which equals $g$ directly (no factor of two).
Add the highlighted method to your notes before the check below.
Quick check: True or false: in the velocity–time method, the gradient of the graph gives $g$ directly without multiplying by two.
Pattern B, Plan, measure, evaluate
Your group drops a steel ball and analyses video frames. In your book: (1) describe how you would collect data for both the $s$-vs-$t^2$ graph and the v–t graph; (2) state how to extract $g$ from each gradient; (3) suggest one source of error and whether it is random or systematic.
Fill the gaps. Plotting $s$ against $t^2$ for a falling object gives a straight line of gradient . Plotting $v$ against $t$ gives a straight line of gradient . Repeating a measurement improves its .
Dot point: Conduct a laboratory experiment to compare 2 methods of graphically determining a value for acceleration due to gravity and assess the accuracy and reliability of the experimental results
The scientific payoff: judging how good your two values are
We just learned two ways to get $g$. That raises a question: once you have two values, how do you judge which experiment was better? This card answers it → by assessing accuracy against the true value and reliability across repeats.
A good experiment is judged on two separate things: how close your value sits to the accepted $9.8\ \text{m s}^{-2}$ (accuracy) and how consistent your repeated runs are with each other (reliability).
Compare each value to the accepted $g = 9.8\ \text{m s}^{-2}$: a smaller percentage difference means greater accuracy. Repeat each method several times: closely grouped repeats mean greater reliability. A method that is reliably wrong (tight grouping, but off the true value) signals a systematic error, for example air resistance always making $g$ read low, or a ticker-timer running fast. The velocity–time method is often more accurate because plotting many points averages out random timing errors.
Assess accuracy by the percentage difference from the accepted $g = 9.8\ \text{m s}^{-2}$, and reliability by how closely repeats agree. A reliable but inaccurate result points to a systematic error (e.g. air resistance, a mistimed timer), which more repeats cannot remove.
Pause, copy the highlighted assessment criteria into your book before the check below.
Last check: Decide if the statement is true or false.
A set of results that are consistent with each other but consistently below the accepted value of $g$ indicates a systematic error.
Match each experimental issue with what it affects:
Dot point: Conduct a laboratory experiment to compare 2 methods of graphically determining a value for acceleration due to gravity and assess the accuracy and reliability of the experimental results
A fresh set drawn from this lesson's question bank, feedback shown immediately. +5 XP per correct · +25 XP all correct
Pick your answer, then rate your confidence, that tells the system what to drill next.
EvaluateBand 6(4 marks) 1. A student measures $g$ using a $v$–$t$ graph and obtains $9.6\ \text{m s}^{-2}$, repeated three times with values $9.5$, $9.6$ and $9.7\ \text{m s}^{-2}$. Assess the accuracy and reliability of these results and identify a likely source of any difference from the accepted value.
1 mark: reliable (repeats close together) · 1 mark: reasonably accurate (close to $9.8\ \text{m s}^{-2}$) · 1 mark: small consistent under-reading suggests a systematic error · 1 mark: names a plausible cause (e.g. air resistance / timing delay)
AnalyseBand 6(4 marks) 2. A student determines $g$ by two graphical methods: plotting $s$ against $t^2$, and plotting $v$ against $t$. Explain how $g$ is obtained from each gradient, and identify one reason the two values might differ.
1 mark: $s$ vs $t^2$ has gradient $g/2$, so $g = 2 \times$ gradient · 1 mark: $v$ vs $t$ has gradient $g$ directly · 1 mark: both use a line of best fit, not a single point · 1 mark: a valid reason for a difference, such as air resistance or timing error affecting one method more
Dot point: Conduct a laboratory experiment to compare 2 methods of graphically determining a value for acceleration due to gravity and assess the accuracy and reliability of the experimental results
EvaluateBand 6(3 marks) 3. Distinguish between the accuracy and the reliability of a measurement of $g$, and state one change that improves each.
1 mark: accuracy is closeness to the true value · 1 mark: reliability is consistency of repeats · 1 mark: one valid improvement for each
Dot point: Conduct a laboratory experiment to compare 2 methods of graphically determining a value for acceleration due to gravity and assess the accuracy and reliability of the experimental results
MC answers and full explanations are shown inline as you complete each question. Use the retry button to attempt a fresh set from the lesson bank.
Q1 (4 marks): The results are reliable because the three repeats ($9.5$, $9.6$, $9.7\ \text{m s}^{-2}$) are tightly grouped, differing by only $0.2\ \text{m s}^{-2}$. They are also reasonably accurate, since $9.6\ \text{m s}^{-2}$ is close to the accepted value of $9.8\ \text{m s}^{-2}$ (about a $2\%$ difference). However, every reading is slightly below $9.8$, and a consistent under-reading like this points to a systematic error rather than random scatter. A likely cause is air resistance acting on the falling object (which reduces its acceleration below $g$), or a small delay in the timing equipment. More repeats would not remove this bias; reducing air resistance or recalibrating the timer would.
Q2 (4 marks): From $s = ut + \tfrac{1}{2}at^2$ with $u = 0$, $s = \tfrac{1}{2}gt^2$, so a graph of $s$ against $t^2$ is a straight line through the origin with gradient $g/2$; the value of $g$ is therefore twice the gradient. From $v = u + at$ with $u = 0$, $v = gt$, so a graph of $v$ against $t$ is a straight line through the origin whose gradient is $g$ directly. In both cases the gradient is taken from a line of best fit through all the points, not from one pair of readings. The two values may differ because the methods are not equally sensitive to the same errors: air resistance removes more from the later, faster part of the motion, which distorts the $v$ against $t$ gradient more, while a constant timing offset shifts the $s$ against $t^2$ line without changing its gradient as much.
Q3 (3 marks): Accuracy is how close a measured value is to the accepted true value, here $9.8\ \text{m s}^{-2}$. Reliability is how consistently the experiment reproduces the same value when repeated under the same conditions. They are independent: a badly calibrated timer can give ten readings that agree closely with each other, which is reliable and inaccurate. Accuracy is improved by removing systematic error, for example by using a dense compact object so air resistance is negligible, or by calibrating the timer. Reliability is improved by repeating each drop several times and averaging, and by using light gates rather than a hand-operated stopwatch so that random human reaction time is removed from every reading.
You can now determine $g$ from two graphical methods and judge your results for accuracy and reliability. Next lesson returns to vectors with a twist: relative velocity, where motion is measured from a moving frame of reference.
↩ Back to focus-area hubAt the start, two groups got $9.6$ and $10.3\ \text{m s}^{-2}$. The $9.6$ is closer to the true $9.8\ \text{m s}^{-2}$, so it is more accurate. But you cannot decide which method to trust from one run alone, you need repeats to judge reliability and to spot systematic errors. Revisit Card 3 if accuracy and reliability still feel like the same thing.
A short spaced-retrieval set, mixing this lesson with earlier ones. It gets harder to guess and easier to remember.
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