An electromagnetic launcher sled is decelerating on a straight, horizontal test track. The sled is initially cruising at a constant speed of $40{m\; s}^{-1}$. When an emergency stop command is initiated, there is a system telemetry delay of $0.25s$ before the mechanical friction brakes engage. The total stopping distance of the sled, measured from the exact instant the stop command is initiated, is $110m$.

Calculate the magnitude of the constant deceleration of the sled while the friction brakes are active.

A physics researcher slides a polymer puck of mass $M$ across a high-friction synthetic sheet to investigate the constant resistive force $F$ opposing its motion.

The researcher wishes to investigate how the total sliding distance $x$ before the puck comes to rest depends on its initial projection speed $v$.

The initial speed $v$ and distance $x$ are related by the work-energy equation:

$$\frac{1}{2}M{v}^2=Fx$$

• Describe how an experiment can be conducted in the laboratory to investigate the relationship between $v$ and $x$.
• Explain how the experimental data can be analysed to determine the resistive force $F$, assuming the mass $M$ is known.