Total time of travel?

Classical Mechanics Level 2

A particle starts from rest and moves along a straight line with uniform acceleration . It's displacement in the first 3 seconds is equal to its displacement in the last second . Its total time of travel is __________ \text{\_\_\_\_\_\_\_\_\_\_} seconds.


The answer is 5.

Abhiram Rao by Abhiram Rao , 18, India

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1 solution

s = u t + 1 2 a t 2 s=ut+\dfrac 1 2 at^2 . Displacement in first 3 3 seconds is s = 9 a 2 s=\dfrac{9a} 2 .

Displacement of the particle in the nth second is s = a 2 ( 2 n − 1 ) s=\dfrac a 2 (2n-1) . Here, we take n as the last second.

We have 9 a 2 = a 2 ( 2 n − 1 ) \dfrac{9a} 2=\dfrac a 2 (2n-1) or n = 5 n=5 .

Hence total time of travel is 5 5 seconds.

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