**Solution:**

Given:
- The machine gun fires 10 bullets per second.
- The velocity of each bullet is 500 m/s.
- The mass of each bullet is 10 grams.

We need to find the acceleration produced in the vehicle.

**Step 1: Convert mass to kg**
- The mass of each bullet is given as 10 grams.
- 1 kilogram (kg) is equal to 1000 grams.
- Therefore, the mass of each bullet in kilograms is 10 grams / 1000 = 0.01 kg.

**Step 2: Calculate the momentum of each bullet**
- The momentum of an object is given by the formula: momentum = mass x velocity.
- The mass of each bullet is 0.01 kg and the velocity is 500 m/s.
- Therefore, the momentum of each bullet is 0.01 kg x 500 m/s = 5 kg.m/s.

**Step 3: Calculate the total momentum of the bullets fired per second**
- Since the gun fires 10 bullets per second, the total momentum of the bullets fired per second is 10 x 5 kg.m/s = 50 kg.m/s.

**Step 4: Use Newton's second law of motion**
- Newton's second law of motion states that force = mass x acceleration.
- Rearranging the formula, acceleration = force / mass.

**Step 5: Calculate the force exerted by the bullets on the vehicle**
- The force exerted by the bullets on the vehicle is equal to the change in momentum per second.
- Since the vehicle is initially at rest, the change in momentum per second is equal to the total momentum of the bullets fired per second.
- Therefore, the force exerted by the bullets on the vehicle is 50 kg.m/s.

**Step 6: Calculate the acceleration of the vehicle**
- The mass of the vehicle is given as 2 quintals.
- 1 quintal is equal to 100 kg.
- Therefore, the mass of the vehicle is 2 quintals x 100 kg/quintal = 200 kg.
- Using the formula acceleration = force / mass, the acceleration of the vehicle is 50 kg.m/s / 200 kg = 0.25 m/s^2.

**Step 7: Convert the acceleration to cm/s^2**
- 1 m/s^2 is equal to 100 cm/s^2.
- Therefore, the acceleration of the vehicle is 0.25 m/s^2 x 100 cm/s^2 = 25 cm/s^2.

Therefore, the acceleration produced in the vehicle is 25 cm/s^2.