\section*{Task 1 - 011131}

A motor vehicle traveling at a speed of \(90 \frac{\mathrm{km}}{\mathrm{h}}\) is braked and comes to a stop after 70 \(\mathrm{m}\).

Has the prescribed deceleration of at least \(4.0 \frac{\mathrm{m}}{\mathrm{s}^{2}}\) in the Road Traffic Regulations been observed or not? Justify your conclusion!
}

From the known formulas for uniformly accelerated motion \(\Delta s=\frac{1}{2} a t^{2}+v_{0} t\) and \(\Delta v=a t\), it follows that

\[
\Delta s=\frac{-v_{0}}{2} t+v_{0} t \Rightarrow t=\frac{2 \Delta s}{v_{0}} \Rightarrow a=-\frac{v_{0}^{2}}{2 \Delta s}
\]

With the given values \(v_{0}=90 \frac{\mathrm{km}}{\mathrm{h}}=25 \frac{\mathrm{m}}{\mathrm{s}}\) and \(\Delta s=70 \mathrm{~m}\), the braking deceleration \(-a \approx 4.464 \frac{\mathrm{m}}{\mathrm{s}^{2}}\), meaning the prescribed braking deceleration was met.