When a potential difference is applied across the ends of a linear metallic conductor
A. The free electrons are accelerated continuously from the lower potential end to the higher potential end of the conductor
B. The free electrons are accelerated continuously from the higher potential end to the lower potential end of the conductor
C. The free electrons acquire a constant drift velocity from the lower potential end to the higher potential end of the conductor
D. The free electrons are set in motion from their position of rest

Hint: When electric potential difference is applied then there is electric field inside the metallic conductor. When a charge is kept in an electric field then it experiences electric force.

Complete step by step solution:
When a potential difference is applied across the ends of a linear metallic conductor then one end of the conductor is at lower potential and other should be at higher potential. If the applied potential difference is constant. Then the potential gradient inside the conductor will be constant. The change in potential difference per unit horizontal distance is equal to the negative of the electric field vector. So the electric field inside the conductor is from higher potential to the lower potential.

In metallic conductors the free electrons are in random motion when potential difference is zero. When the potential difference is applied then the electric field gets inside the conductor. The electric force is applied on the free electrons in the direction opposite to the direction of the electric field vector, i.e. from lower higher potential to the lower potential. Hence, the free electrons acquire drift velocity from the lower potential end to the higher potential end of the conductor.

Therefore, the correct option is C.

Note: As there is force acting on the free electron, so there is acceleration in it. But during the motion it encounters collisions with the neighbouring free electrons. Hence, the acceleration is not continuous.