Question

The velocity of a particle moving along the xaxis is given by `v=v_(0)+lambdax`, where `v_(0)` and lambda are constant. Find the velocity in terms of t.

Answer 1

`v=v_(0)+lambdax`
`(dv)/(dt)=0+lambda(dx)/(dt)=lambdav`
`a=lambdav`
At `x=0, v=v_(0)`
`a=lambdav`
`(dv)/(dt)=lambdav`
`int_(v_(0))^(v)(dv)/v=lambda int_(0)^(t) dt`
`|log_(e)v|_(v_(0))^(v)=lambda|t|_(0)^(t)`
`log_(e)v-log_(e)v_(0)=lambdat`
`log_(e)(v/v_(0))=lambdat`
`v/v_(0)=e^(lambdat)`
`v=v_(0)e^(lambdat)`