Train 2

A metro train moved between neighbouring stations as follows: it gradually accelerated and reached a speed of 70 km/h in 10 seconds. It then travelled at this speed for 35 seconds. Finally, it decelerated for 15 seconds until it stopped. Draw the speed-time graph and calculate the distance between the stations.

Final 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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