**Problem Statement:**
An object is thrown vertically up from the ground and passes a height of 5m twice in an interval of 10s. We need to determine the time of flight for this object.

**Solution:**

To solve this problem, let's break it down into smaller steps:

**Step 1:**
Understand the motion of the object:
- The object is thrown vertically up from the ground, which means its initial velocity is positive.
- The object reaches a maximum height and then falls back towards the ground due to gravity.
- The object passes a height of 5m twice, so it reaches a height of 5m during its upward journey and then again during its downward journey.

**Step 2:**
Determine the time taken to reach a height of 5m during the upward journey:
- Let's assume the time taken to reach a height of 5m during the upward journey is t1.
- During this time, the object is moving against gravity, so its acceleration is -9.8 m/s^2.
- Using the equation of motion: h = ut + (1/2)at^2, where h is the height, u is the initial velocity, a is the acceleration, and t is the time, we can write the equation as: 5 = u(t1) + (1/2)(-9.8)(t1)^2.

**Step 3:**
Determine the time taken to reach a height of 5m during the downward journey:
- Let's assume the time taken to reach a height of 5m during the downward journey is t2.
- During this time, the object is moving with gravity, so its acceleration is +9.8 m/s^2.
- Using the equation of motion: h = ut + (1/2)at^2, where h is the height, u is the initial velocity, a is the acceleration, and t is the time, we can write the equation as: 5 = u(t2) + (1/2)(9.8)(t2)^2.

**Step 4:**
Determine the time of flight:
- The time of flight is the total time taken by the object from the moment it is thrown up until it reaches the ground again.
- The total time of flight can be calculated by adding the time taken during the upward journey (t1) and the time taken during the downward journey (t2).
- Therefore, the time of flight = t1 + t2.

**Step 5:**
Solve the equations to find the time of flight:
- We have two equations from Step 2 and Step 3, and we need to solve them simultaneously to find t1 and t2.
- Once we have the values of t1 and t2, we can calculate the time of flight by adding them together.

**Step 6:**
Finalize the solution:
- Substitute the values of t1 and t2 into the equation for the time of flight (t1 + t2) to get the final answer.
- Make sure to include the appropriate units for the time of flight (seconds).

In conclusion, by following the above steps, we can determine the time of flight for the object thrown vertically up from the ground.

20 sec