Question

a body of mass 2kg initially at rest on a smooth horizontal plane is subjected to a horizontal forve of magnitude 1/2v+1. find the time when the velocity is 1ms

Answer 1

$F=ma=m\frac{dv}{dt},$

$\frac 1{2v+1}=2\frac{dv}{dt},$

$(4v+2)dv=dt,$

$t(v)=2v^2+2v,$

$t(1)=4~s.$