Question

The initial velocity of a particle moving along x axis is u(at 0 and 0) and its acceleration a is given by a kx. Which of the following equation is correct between its velocity(v) and position(x)?
(a)v2-u2=2kx
(b)v2=u2+2kx2
(c)v2=u2+kx2
(d)v2+u2=2kx

Answer 1

a = kx  

a= dv/dt = [dv/dx]*[dx/dt]  

a = vdv/dx  

vdv = adx  

vdv = kxdx  

v^2/2 = k*x^2/2 + C  

as at t = 0 , x = 0 and velocity = u  

so C = u^2/2  

v^2/2 = kx^2/2 + u^2/2  

v^2 = u^2 + kx^2

Answer 2

Answer:

a = kx  

a= dv/dt = [dv/dx]*[dx/dt]  

a = vdv/dx  

vdv = adx  

vdv = kxdx  

v^2/2 = k*x^2/2 + C  

as at t = 0 , x = 0 and velocity = u  

so C = u^2/2  

v^2/2 = kx^2/2 + u^2/2  

v^2 = u^2 + kx^2

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