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```        the velocity of the particle noving in the x-y plane is given by dx/dt=8asin2at,dy/dt=5acos2at.when t=0,x=8andy=0,the path of the particle is a.................here a=3.14
sir plz tell some 2 way to find path of particle```
7 years ago

147 Points
```										Dear jauneet
to find the path means you have to find the ralation ship between x and y with the given information .
here we have to eleminate the t .
dx/dt=8asin2at
intigrate
x= -(8acos2at )/2a   + c1
x = -4cos2at + c1
now use the given condition
at t=0 ,x=8
so 8=-4 +c1
c1=12
so equation become
x =-4cos2at  + 12
or  (x-12)/4 = -cos2at ............1
now similerly for y
dy/dt=5acos2at
intigrate
y= (5asin2at)/2a  +c2
y =5/2 sin2at + c2
now apply condition
y=0 at t=0
0 =0+c2
c2=0
so equation become
y  =5/2 sin2at
or 2y/5 = sin2at ............2

now square equation 1 and 2 and add
((x-12)/4)2 + (2y/5)2 = 1
this the path of the article
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7 years ago
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