Two object, each of mass `1.5 kg`, are moving in the same straight line but in opposite directions, The velocity of each object is `2.5 ms^(-1)` before the collision during which they stick together. What will be the velocity of the combined object after collision?

Explanation

To solve the problem, we will apply the principle of conservation of linear momentum. Here are the steps:

### Step 1: Identify the masses and velocities of the objects
- Mass of object 1 (m1) = 1.5 kg
- Velocity of object 1 (v1) = 2.5 m/s (to the right)
- Mass of object 2 (m2) = 1.5 kg
- Velocity of object 2 (v2) = -2.5 m/s (to the left, hence negative)

### Step 2: Write the equation for conservation of momentum
The total momentum before the collision must equal the total momentum after the collision. The equation is:
\[ m_1 v_1 + m_2 v_2 = (m_1 + m_2) v \]
Where \( v \) is the velocity of the combined object after the collision.

### Step 3: Substitute the known values into the equation
Substituting the values we have:
\[ (1.5 \, \text{kg}) \cdot (2.5 \, \text{m/s}) + (1.5 \, \text{kg}) \cdot (-2.5 \, \text{m/s}) = (1.5 \, \text{kg} + 1.5 \, \text{kg}) \cdot v \]

### Step 4: Calculate the left side of the equation
Calculating the left side:
\[ 1.5 \cdot 2.5 = 3.75 \, \text{kg m/s} \]
\[ 1.5 \cdot (-2.5) = -3.75 \, \text{kg m/s} \]
So,
\[ 3.75 - 3.75 = 0 \]

### Step 5: Set the equation to solve for v
Now we have:
\[ 0 = (3 \, \text{kg}) \cdot v \]

### Step 6: Solve for v
Dividing both sides by 3 kg:
\[ v = 0 \, \text{m/s} \]

### Conclusion
The velocity of the combined object after the collision is **0 m/s**.

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