Consider two observers moving with respect to each other at a speed v along a straight line. They observe a block of mass m moving a distance l on a rough surface. The following quantities will be same as observed by the two observers

Options

A. kinetic energy of the block t tiem t
B. work doen by friction
C. total work done the block
D. accelertion of the block

Answer

To solve the problem, we need to analyze the quantities observed by two observers moving with respect to each other at a constant speed. We will evaluate each quantity mentioned in the question to determine which one remains the same for both observers.

### Step-by-Step Solution:

1. **Understanding the Observers**:
- We have two observers moving with respect to each other at a constant speed \( v \).
- They are observing a block of mass \( m \) moving a distance \( l \) on a rough surface.

2. **Kinetic Energy**:
- The kinetic energy \( KE \) of the block is given by the formula:
\[ KE = \frac{1}{2} m v^2 \]
- The mass \( m \) is a frame-independent quantity, but the velocity \( v \) of the block depends on the observer's frame of reference. Therefore, the kinetic energy will differ for the two observers.

3. **Work Done by Friction**:
- The work done \( W \) by friction is calculated as:
\[ W = F \cdot d \]
where \( F \) is the frictional force and \( d \) is the displacement.
- The frictional force \( F \) is frame-independent, but the displacement \( d \) is frame-dependent. Thus, the work done by friction will also differ for the two observers.

4. **Total Work Done**:
- The total work done on the block is the sum of the work done by all forces acting on it.
- Since the work done by any force depends on the displacement (which is frame-dependent), the total work done will also vary between the two observers.

5. **Acceleration**:
- The acceleration \( a \) of the block can be analyzed using the relative motion concept.
- The relative acceleration between two observers moving at constant velocity is zero:
\[ a_{\text{relative}} = a_{\text{block}} - a_{\text{observer}} = 0 \]
- Since both observers are moving with constant velocity, they will observe the same acceleration of the block.

### Conclusion:
After analyzing all the quantities, we find that the only quantity that remains the same for both observers is the **acceleration of the block**.

### Final Answer:
The quantity that will be the same as observed by the two observers is the **acceleration of the block**.

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