Particle A is moving along X-axis. At time t = 0, it has velocity of `10 ms^(-1)` and acceleration `-4ms^(-2)`. Particle B has velocity of `20 ms^(-1)` and acceleration `-2 ms^(-2)`. Initially both the particles are at origion. At time t = 2 distance between the particles are at origin. At time t = 2 s distance between the particles is

Options

A. 24 m
B. 36 m
C. 20 m
D. 42 m

Explanation

To solve the problem, we need to find the positions of both particles A and B at time \( t = 2 \) seconds and then calculate the distance between them.

### Step 1: Calculate the position of Particle A at \( t = 2 \) seconds
The formula for the position \( s \) of a particle under uniform acceleration is given by:

\[ s = ut + \frac{1}{2} a t^2 \]

For Particle A:
- Initial velocity \( u_A = 10 \, \text{m/s} \)
- Acceleration \( a_A = -4 \, \text{m/s}^2 \)
- Time \( t = 2 \, \text{s} \)

Substituting the values into the formula:

\[ s_A = 10 \cdot 2 + \frac{1}{2} \cdot (-4) \cdot (2^2) \]

Calculating this step-by-step:

1. Calculate \( 10 \cdot 2 = 20 \)
2. Calculate \( (2^2) = 4 \)
3. Calculate \( \frac{1}{2} \cdot (-4) \cdot 4 = -8 \)
4. Combine the results: \( s_A = 20 - 8 = 12 \, \text{m} \)

### Step 2: Calculate the position of Particle B at \( t = 2 \) seconds
For Particle B:
- Initial velocity \( u_B = 20 \, \text{m/s} \)
- Acceleration \( a_B = -2 \, \text{m/s}^2 \)
- Time \( t = 2 \, \text{s} \)

Using the same formula:

\[ s_B = 20 \cdot 2 + \frac{1}{2} \cdot (-2) \cdot (2^2) \]

Calculating this step-by-step:

1. Calculate \( 20 \cdot 2 = 40 \)
2. Calculate \( (2^2) = 4 \)
3. Calculate \( \frac{1}{2} \cdot (-2) \cdot 4 = -4 \)
4. Combine the results: \( s_B = 40 - 4 = 36 \, \text{m} \)

### Step 3: Calculate the distance between the two particles
Now that we have the positions of both particles:

- Position of Particle A: \( s_A = 12 \, \text{m} \)
- Position of Particle B: \( s_B = 36 \, \text{m} \)

The distance between the two particles is:

\[ \text{Distance} = s_B - s_A = 36 - 12 = 24 \, \text{m} \]

### Final Answer
The distance between the particles at \( t = 2 \) seconds is \( 24 \, \text{m} \).

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