A train is moving with a velocity of 54 kmph. It is accelerated at the rate 5m/s2. Find the distance travelled by the train in the 5th second of its journey.A 30 m B 37.5 m C 40 m D 47.5 m
Question
A train is moving with a velocity of 54 kmph. It is accelerated at the rate 5m/s2. Find the distance travelled by the train in the 5th second of its journey.A 30 m B 37.5 m C 40 m D 47.5 m
Solution
To solve this problem, we need to use the formula for distance travelled in nth second which is given by:
s_n = u + a/2(2n-1)
where: s_n is the distance travelled in nth second, u is the initial velocity, a is the acceleration, and n is the nth second.
However, before we can use this formula, we need to convert the initial velocity from kmph to m/s. We can do this by multiplying the kmph value by 5/18.
So, the initial velocity u in m/s is 54 * 5/18 = 15 m/s.
Now we can substitute the values into the formula:
s_5 = 15 + 5/2(2*5 - 1) s_5 = 15 + 2.5(9) s_5 = 15 + 22.5 s_5 = 37.5 m
So, the train travels 37.5 meters in the 5th second of its journey. The correct answer is B) 37.5 m.
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