Linearise a dataset that suggests a non-linear relationship (e.g. t2 versus s) and calculate the equation of the linear trend line.

A student investigates the motion of a falling object and records displacement \( s \) at different times \( t \). Analysis of the raw data suggests a quadratic relationship \( s = at^2 \). To linearise the data, the student plots \( s \) against \( t^2 \) and calculates a line of best fit with gradient \( m = 4.85\,\text{m}\,\text{s}^{-2} \) and \( y \)-intercept \( c = 0.12\,\text{m} \). What is the best interpretation of the non-zero intercept?

A student measures the displacement s of a trolley at different times t. The relationship between s and t is non-linear. Which transformation of the dataset will produce a linear relationship?

A student investigates the relationship between time \( t \) and displacement \( s \) for an accelerating trolley and records the data below. Refer to the table below. Which plot will produce a linear graph?