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...