A high-speed pneumatic capsule is travelling along a straight horizontal tube at a constant speed of $32{m\; s}^{-1}$. An emergency braking command is sent, but there is a system latency (reaction time) of $0.15s$ before the mechanical brakes engage. The total distance travelled from the moment the command is sent until the capsule comes to rest is $84.8m$.

Calculate the magnitude of the deceleration of the capsule once the brakes engage.

A student launches a mechanical glider of mass $m$ at various initial speeds $u$ along a horizontal track. A small friction pad on the underside of the glider provides a constant frictional force $f$ that eventually brings the glider to rest over a sliding distance $s$.

The initial speed $u$ and sliding distance $s$ are related by the equation

$$\frac{1}{2}m{u}^2=fs$$

• Describe how an experiment can be conducted in the laboratory to investigate the relationship between $u$ and $s$.
• Explain how the data can be analysed to determine $f$.