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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
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B
4050 m
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C
8100 m
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D
1250 m
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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 velocity
u = initial velocity
a = acceleration
t = time
Put the value into the equation

Finally 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 = distance
v = final velocity
u = initial velocity
a = acceleration
t = time
Put the value into the equation

Where 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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