Train - start-up

A train weighing 1200 tons is supposed to reach a speed of 15 m/s in 45 s when starting up. Determine its acceleration and the magnitude of the force it must exert if the friction force is 0.005 of the train's gravity.

Correct answer:

a =  0.3333 m/s²
F =  60000 N

Step-by-step explanation:

$$\begin{gathered} t=45\text{s} \\ v=15\text{m/s} \\ v=a\cdot t \\ a=v/t=15/45=0.3333{\text{m/s}}^2 \end{gathered}$$

$$\begin{gathered} m=1200\text{t}\to \text{kg}=1200\cdot 1000\text{kg}=1200000\text{kg} \\ g=10{\text{m/s}}^2 \\ k=0.005 \\ G=m\cdot g=1200000\cdot 10=12000000\text{N} \\ F=k\cdot G=0.005\cdot 12000000=60000\text{N} \end{gathered}$$

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