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Find the equation of trajectory of a par...

Find the equation of trajectory of a particle whose velocity components are
`v_(x)=2x+1, v_(y)=2y+3`
Given that particle starts from rest from origin.

Text Solution

Verified by Experts

`v_(x)=2x+1`,
`(dx)/(dt)=2x+1`
`int_(0)^(x) (dx)/(2x+1)=int_(0)^(t)dt`
`(1)/(2)ln(2x+1)=t " "` ....(1)
`v_(y)=2y+3`
`int _(0)^(y)(dy)/(2y+3)=int_(0)^(t)dt`
`(1)/(2) "ln "((2y+3))/(3)=t" "` ...(2)
from (1) and (2)
`(1)/(2) ln (2x+1)=(1)/(2) "ln" ((2y+3))/(3)`
`2x+1=((2y+3))/(3)`
`y=3x`
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