A particle is dropped from a vertical height h and falls freely for a time t. With the aid of a sketch, explain how h varies with \(t^2\)
For a particle dropped from rest, the initial velocity, \(u=0\), and the acceleration is \(g\).
Using the equation of motion,
\[h=ut+\frac{1}{2}gt^2\]
\[h=\frac{1}{2}gt^2\]
Thus, \(h\) is directly proportional to \(t^2\). A plot of \(h\) on the vertical axis against \(t^2\) on the horizontal axis is a straight line passing through the origin.
Graph of height fallen, h, against t² for a freely falling particle. The straight line passes through the origin and has gradient g/2.
For a particle dropped from rest, the initial velocity, \(u=0\), and the acceleration is \(g\).
Using the equation of motion,
\[h=ut+\frac{1}{2}gt^2\]
\[h=\frac{1}{2}gt^2\]
Thus, \(h\) is directly proportional to \(t^2\). A plot of \(h\) on the vertical axis against \(t^2\) on the horizontal axis is a straight line passing through the origin.
Graph of height fallen, h, against t² for a freely falling particle. The straight line passes through the origin and has gradient g/2.