  Question

A train is travelling at a speed of $$90\ km\ h^{-1}$$. Brakes are applied so as to produce a uniform acceleration of $$-0.5\ ms^{-2}$$. Find how far the train will go before it is brought to rest?

A
625 m  B
4050 m  C
8100 m  D
1250 m  Solution

The correct option is A $$625\ m$$Given that,Acceleration $$a = -0.5 m/s^2$$Speed $$v = 90 km/h=25 m/s$$Using equation of motion, $$v = u + at$$Where, v = final velocityu = initial velocitya = accelerationt = timePut the value into the equationFinally train will be rest so, final velocity,$$v = 0$$$$0 = 25 - 0.5t$$$$25 = 0.5t$$$$t = \dfrac{25}{0.5}$$$$t = 50\ sec$$Again, using equation of motion, $$S = ut + \dfrac{1}{2}at^2$$Where, s = distancev = final velocityu = initial velocitya = accelerationt = timePut the value into the equationWhere S is distance travelled before stop$$s = 25\times50-\dfrac{1}{2}\times0.5\times(50)^2$$$$s = 625\ m$$So, the train will go before it is brought to rest is $$625\ m$$.Hence, A is correct.Physics

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