To solve this problem, we can use the equations of motion. Let's break down the problem step by step:

1. Determine the time taken by Akshat to reach the destination:
- Akshat starts moving with a velocity of 20 m/s.
- The distance to be covered is 1000 m.
- We can use the equation: distance = velocity × time
- Plugging in the values, we get 1000 = 20 × time
- Solving for time, we find that Akshat takes 50 seconds to reach the destination.

2. Determine the time taken by Hariom to reach the destination:
- Hariom starts moving 2 seconds after Akshat.
- Therefore, Hariom has a head start of 20 m/s × 2 s = 40 m.
- The remaining distance to be covered by Hariom is 1000 m - 40 m = 960 m.
- We can use the equation: distance = velocity × time
- Plugging in the values, we get 960 = velocity × time
- Since we know the distance and velocity, we need to find the time taken by Hariom.
- We can use the equation: time = distance / velocity
- Plugging in the values, we get time = 960 / velocity

3. Determine the ratio of initial velocities:
- Let the initial velocity of Hariom be Vh and the initial velocity of Akshat be Va.
- We know that Va = 20 m/s.
- To find Vh, we need to determine the time taken by Hariom.
- From step 2, we have time = 960 / velocity. Plugging in the values, we get time = 960 / Vh.
- Since both Akshat and Hariom reach the destination at the same time, we can equate their times: 50 = 960 / Vh.
- Solving for Vh, we find that Vh = 960 / 50 = 19.2 m/s.
- Therefore, the ratio of initial velocities is 20 m/s : 19.2 m/s, which simplifies to 25 : 24.

4. Determine the ratio of accelerations:
- Let the acceleration of Hariom be Ah and the acceleration of Akshat be Aa.
- We are given that the ratio of accelerations is 2:3, which means Ah / Aa = 2/3.
- Since we know the initial velocities and the time taken by both Akshat and Hariom, we can use the equation: distance = initial velocity × time + (1/2) × acceleration × time^2.
- Plugging in the values for Akshat, we get 1000 = 20 × 50 + (1/2) × Aa × 50^2.
- Simplifying the equation, we find 1000 = 1000 + 1250Aa.
- Solving for Aa, we find Aa = 0 m/s^2.
- Since Aa = 0 m/s^2, the acceleration of Akshat is zero.
- Therefore, the acceleration of Hariom is also zero.

In conclusion, the ratio of initial velocities is