Your tutor is correct. Non-balanced forces cause acceleration.
If I push on the wall, I am applying force, but the wall does not move, i.e. it does not change its (rest) motion.
Understand that acceleration is a change in velocity.
Speed is a scalar (quantity).
Velocity is a a vector (quantity and direction).
Acceleration is not defined as a change in speed, but a change in velocity; therefore changing EITHER speed OR direction (or both) is an acceleration.
When physicists watch the trails of charged particles as they pass through magnetic fields, they are seeing the effects you mention. The particles go through spiral-like motions because the acceleration is normal to (perpendicular to) the velocity.
F= Gm1m2 / r^2 is a law, not because its always true, but because it's a description of what we see. However, there is a theory embedded in this law. The theory is that acceleration is always due to an unbalanced force.
