Question about acceleration and movemenr

[danielhaish]

But we know it not true becouse then it was almost impossible to run on a train

 

[kuruman]

100²-100=10,000-100 = 9900.
Also you spend $\frac{1}{2}\times 1~\mathrm{kg}\times 10^2~\mathrm{m^2/s^2}=50~\mathrm{J}.$

 

[A.T.]

But we know it not true becouse then it was almost impossible to run on a train

In the frame of the ground the train is doing positive work on you, if you accelerate forward while running in the train. You spend the same energy as on the ground, but the work done by the train on you accounts for the different gain in kinetic energy.

 

[russ_watters]

...though if you tried to run on an accelerating train you would find it difficult.

 

[kuruman]

...though if you tried to run on an accelerating train you would find it difficult.

A little difficult. It would be like running up a plane inclined at angle $\alpha$ relative to the horizontal such that $\sin\alpha=\dfrac{a}{\sqrt{a^2+g^2}}$. For a reasonable acceleration value of 1 m/s² the effective angle is about 6^o or a slope of 10% in the small angle approximation. Piece o' cake for a person in reasonably good shape. Reaching a final speed of 10 m/s is another issue. The 100 m dash world record time (Usain Bolt) now stands at 9.58 s, and that's on level ground.