**Given information:**
- Akshar and Hariom are moving towards a destination that is 1000 m away.
- Akshar's velocity is 20 m/s.
- After 2 seconds, both Akshar and Hariom reach the destination.
- The ratio of their initial velocities is 2:3.

**Step 1: Calculating the time taken by Akshar to reach the destination**
- We know the distance traveled by Akshar is 1000 m and his velocity is 20 m/s.
- Using the formula: distance = velocity × time, we can find the time taken by Akshar.
- Substituting the values, we have 1000 = 20 × time.
- Solving the equation, we find time = 50 seconds.
- Therefore, Akshar takes 50 seconds to reach the destination.

**Step 2: Calculating the time taken by Hariom to reach the destination**
- We know that Hariom reaches the destination after 2 seconds of Akshar.
- Therefore, Hariom's time taken to reach the destination is 50 - 2 = 48 seconds.

**Step 3: Calculating the initial velocity of Hariom**
- We know that the ratio of their initial velocities is 2:3.
- Let's assume Akshar's initial velocity as 2x m/s.
- Therefore, Hariom's initial velocity will be 3x m/s.

**Step 4: Calculating the initial acceleration**
- We need to find the initial acceleration of both Akshar and Hariom.
- The acceleration can be calculated using the formula: acceleration = (final velocity - initial velocity) / time taken.
- We already know the time taken by Akshar and Hariom.
- The final velocity of both Akshar and Hariom is 20 m/s (as they reach the destination with the same velocity).
- Substituting the values, we have acceleration = (20 - 2x) / 50 = (20 - 3x) / 48.
- Therefore, the ratio of their initial acceleration is (20 - 2x) : (20 - 3x).

In summary, the ratio of initial velocities is 2:3 and the ratio of initial accelerations is (20 - 2x) : (20 - 3x).