I'm attempting to solve a problem where the torque of a motor varies with RPM linearly. I've done most of the groundwork, and come up with this equation for how acceleration would vary with the speed of the vehicle
a = -1.2503v + 1.4533
From this and F = ma, I think I should come up with the following differential equation:
m dv/dt = -1.2503v + 1.4533
From there, I'm a bit stumped...
You are given a, the acceleration, not the force, so there should be no "m" in the equation.
The simplest way to solve is to write it as
and integerate both sides. On the left you will want to make the substitution [tex]u= 1.4533- 1.2503v[tex].