Train 2

A metro train moved between neighboring stations in such a way that it gradually accelerated and in 10 seconds reached a speed of 70 km/h. It then traveled at this speed evenly for 35 seconds. Finally, it slowed down for 15 seconds until it stopped. Draw the time course of the speed on the graph and calculate the distance between the stations.

Correct answer:

x =  923.6111 m

Step-by-step explanation:

$$\begin{gathered} t_1=10\text{s} \\ {v}_1=70\text{km/h}\to \text{m/s}=70:3.6\text{m/s}=19.44444\text{m/s} \\ {t}_2=35\text{s} \\ {t}_3=15\text{s} \\ {a}_1=v_1/t_1=19.4444/10=\frac{35}{18}\doteq 1.9444{\text{m/s}}^2 \\ {a}_2=v_1/t_3=19.4444/15=\frac{35}{27}\doteq 1.2963{\text{m/s}}^2 \\ {s}_1=\frac{1}{2}\cdot a_1\cdot t_1^2=\frac{1}{2}\cdot 1.9444\cdot 10^2=\frac{875}{9}\doteq 97.2222\text{m} \\ {s}_2=v_1\cdot t_2=19.4444\cdot 35=\frac{6125}{9}\doteq 680.5556\text{m} \\ {s}_3=\frac{1}{2}\cdot a_2\cdot t_3^2=\frac{1}{2}\cdot 1.2963\cdot 15^2=\frac{875}{6}\doteq 145.8333\text{m} \\ x=s_1+s_2+s_3=97.2222+680.5556+145.8333=923.6111\text{m} \end{gathered}$$

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