a car starts from rest. when it is at a distance s from its starting point its speed

[markosheehan]

a car starts from rest. when it is at a distance s from its starting point its speed is v and its acceleration is 25v+v³. show that dv=(25+v²)ds and find (correct to 2 decimal places) its speed when s=.01
this is how i went about it
dv/dt= acceleration dv/dt=dv/ds×ds/dt=v×dv/ds

v dv/ds=25v+v³
dv/ds+25+v²
dv=(25+v²)ds i can get this but i do not understand how to get speed when s=.01

 

[Deleted member 4993]

a car starts from rest. when it is at a distance s from its starting point its speed is v and its acceleration is 25v+v³. show that dv=(25+v²)ds and find (correct to 2 decimal places) its speed when s=.01
this is how i went about it
dv/dt= acceleration dv/dt=dv/ds×ds/dt=v×dv/ds

v dv/ds=25v+v³
dv/ds = 25+v²
dv=(25+v²)ds i can get this but i do not understand how to get speed when s=.01

dv/(25+v²) = ds

dv/(5² + v²) = ds

The LHS looks like integration of a standard form [tan^-1(x)]