Analyze Statement I

• Electric force on a charge is $\vec F_e = q\vec E$
• This force can have a component along the velocity of the particle, so it can do work.
• From work-energy theorem, if work is done, kinetic energy changes.

Hence, electric force can change the speed and therefore the kinetic energy of a charged particle.

• Magnetic force on a moving charge is $\vec F_m = q(\vec v \times \vec B)$
• Since $\vec F_m$ is always perpendicular to $\vec v$, the work done by magnetic force is $W = \int \vec F_m \cdot d\vec r = 0$
• Therefore, magnetic force cannot change the kinetic energy of the charged particle; it only changes the direction of motion.

So, Statement I is correct.

Analyze Statement II

• Electric force on a positive charge is along the direction of the electric field: $\vec F_e = q\vec E$

• Therefore, the acceleration of a positive charge is also along $\vec E$, not perpendicular to it.

• Magnetic force on a moving charge is $\vec F_m = q(\vec v \times \vec B)$

• This force is perpendicular to both $\vec v$ and $\vec B$.

• Therefore, magnetic force does not accelerate the particle along the magnetic field.

So, Statement II is incorrect.

Choose the correct option

• Statement I: Correct
• Statement II: Incorrect

Therefore, the correct option is $\boxed{\text{C}}$