In 2007, the French TGV train set a world speed record by achieving a speed of 5

Question

In 2007, the French TGV train set a world speed record by achieving a speed of 575 km/h. At these speeds, most of the engine energy is used to overcome air resistance. The force due to air resistance in a test run was equivalent to the weight of 9.3 tonnes with g = 9.8 m/s2.  The mass of the TGV train was 251 tonnes. During a test run at 535 km/h, the crew decided that they need to stop the train. Assume that they could maintain the 9.3 tonne stopping force constant throughout the braking period. What distance did the train travel from the moment the crew started braking until the train stopped?

1 tonne = 1000 kg

Explanation / Answer

Force due to air resistance = 9300 x 9.8 = 91.14kN

Braking force = 9300 x 9.8 = 91.14 kN

Use v^2 = u^2 + 2as. Here v = 0 and a = 2 x 91.4 x 10^3 / 251000 = 0.7262 m/s^2

u = 148.611 m/s

So, s = 148.611^2/(2*0.7262) = 15206m = 15.206km

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