The acceleration is determined by force \vec{a}=\frac{\vec{F}}{m}.

The acceleration is in general not necerssary pendicular to the velocity.
The Lorentz's force is \vec{F_b}=q\vec{v}\times\vec{B}
For charged particle in uniform magnetic field.
The force \vec{F_B} is always pendicular to both velocity vec{v} and magnetic field \vec{B}.
So the uniform magnetic will only change direction of charged particle (it will not change the speed of charged particle).