Train speed

The train speed is decreased from 72 km/h to 36 km/h in 50 seconds. Assuming that the train movement is continuously slowing, find the acceleration and the distance it travels.

Correct answer:

a =  -0.2 m/a²
s =  750 m

Step-by-step explanation:

$$\begin{gathered} t=50\text{s} \\ {v}_1=72\text{km/h}\to \text{m/s}=72:3.6\text{m/s}=20\text{m/s} \\ {v}_2=36\text{km/h}\to \text{m/s}=36:3.6\text{m/s}=10\text{m/s} \\ a=\frac{v_2-v_1}{t}=\frac{10-20}{50}=-\frac{1}{5}{\text{m/a}}^2=-0.2{\text{m/a}}^2 \end{gathered}$$

$s=v_1\cdot t+\frac{1}{2}\cdot a\cdot t^2=20\cdot 50+\frac{1}{2}\cdot \frac{-1}{5}\cdot 50^2=750\text{m}$

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