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A point moves in a straight line under the retardation av 2 ,where `a’ is a positive constant and v is a speed.If the initial velocity is u,the distance covered in t seconds is:

A point moves in a straight line under the retardation av2,where `a’ is a positive constant and v is a speed.If the initial velocity is u,the distance covered in t seconds is:


 

Grade:12

1 Answers

Chetan Mandayam Nayakar
312 Points
9 years ago

d2x/dt2 =-a(dx/dt)^2, dx/dt= ±(1/a)d2x/dt2, distance covered has meaning for positive values only,thus dx/dt=-d2x/dt2

d2x/dt2 +dx/dt=0,characteristic equation is m^2+m=0,m(m+1)=0,x=c1+c2e-t, two initial values are required, initial position=c1+c2=0(for the sake of simplicity and without loss of generality),dx/dt=u=-c2, at t=0

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