Grade 12th passMechanics

a particle moves rectilinearly. It's displacement x at time t is given by x^2=at^2+b where a and b are constant. Its accelerations at time t is proportional to (a) 1/x^3

Hashim

7 Years agoGrade 12th pass

1 Answer

Arun

7 Years ago

We are given that the displacement of the point is given by the following relation

X2 = 1 + T2 (1)

we know that the acceleration is the double derivative of the displacement. Hence it will be given by d2X / dT2

from equation (1), we get

X = (1 + T2) 1/2

differentiating with respect to T, we get

dX / dT = 1/2 ( 1 + T2) -1/2 x 2T

= T ( 1 + T2) -1/2

d2X / dT2 = 1/ ( 1 + T2)1/2 - T2 / (1+T2) 3/2

But

( 1+ T2)1/2 = X [ from (1)]

Thus

d2X / dT2 = [1/ X ] - [(X2 -1) / X3]

= [X2 -X2 +1] / X3

= 1 / X3

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a particle moves rectilinearly. It's displacement x at time t is given by x^2=at^2+b where a and b are constant. Its accelerations at time t is proportional to (a) 1/x^3

Hashim

1 Answer

Arun

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