Acceleration of a particle is given as a =(2t)i +3j Find the equation of locus.
Answers
Answer:
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Explanation:
Since, x and y components are linearly independent , we can compare them separately on both sides.
Therefore ,
dx/dt = ky OR
dx/ky= dt.
Integrating,
x/ky= t + c1…………….(1).
c1 is constant which can be determine by initial condition.
As initial conditions are not given, for the purpose of generality, we shall assume arbitrarily that
at t= 0, x=xo and y=yo.
Using this conditions in equation (1), we have,
xo/kyo =c1.
Using this value of c1 in equation (1),
x/ky -xo/kyo= t……………..(2)
Similar treatment given to y component yields,
y/kx - yo/kxo = t…………….(3)
Equation of trajectory can be obtained by eliminating t between equations (2) and (3).
So, comparing lhs sides of equations (2) and (3), we get,
x/ky - xo/kyo = y/kx - yo/kxo…………(4).
This is equation of trajectory.
As a special case , if we take xo=yo, then equation (4) will become,
x/y= y/x OR
x^2 -y^2=0. OR
y= + or - x.
These are straight lines starting from point ( xo,yo) and having slopes of +1 or -1.