Writing It Up — practice questions

A student plots $v^2$ against $h$ and obtains a straight line through the origin.

State the type of relationship between $v$ and $h$.

A student plots $v^2$ (m² s⁻²) against $h$ (m) and obtains a straight line through the origin with gradient $19.4$.

Write the mathematical relationship obtained from this data, including the unit of the gradient, and state the relationship between $v$ and $h$.

A student's conclusion reads: "My graph was a straight line, which proves that the period is proportional to the square root of the length, as the theory says."

Evaluate this conclusion and rewrite it to a standard that would earn full credit.

State one variable that should be controlled in an investigation of how the period of a pendulum depends on its length, and state how you would keep it constant.

Explain why there is a practical limit to the smallest value of pendulum length that can usefully be investigated.

In an investigation of how illuminance $E$ from a lamp depends on distance $d$, a student obtained $E = 12/d^2$ but noticed that the points at the largest distances sat consistently above the line on their $E$ against $1/d^2$ graph.

Discuss this unexpected result: suggest a cause, explain how it would produce this specific pattern, and evaluate its effect on the validity of the conclusion.