A box is being pushed horizontally along a rough surface and a constant acceleration is achieved. If the push is stopped, the box will _____

Options

A. slow down and finally stop
B. continue to move at constant speed
C. continue to accelerate at a lower rate
D. stop immediately

Answer

To solve the question, we need to analyze the situation step by step:

1. **Understanding the Initial Condition**: The box is being pushed horizontally along a rough surface, and it has achieved a constant acceleration. This means that the applied force (let's call it F) is greater than the frictional force acting against it (kinetic friction, denoted as f).

2. **Identifying Forces Acting on the Box**: While the box is being pushed, the net force acting on it is the difference between the applied force and the frictional force. Since the box is accelerating, we can say:
\[ F - f = ma \]
where \( m \) is the mass of the box and \( a \) is the acceleration.

3. **Stopping the Push**: Now, if the push is stopped, the applied force F becomes zero. At this point, the only force acting on the box is the kinetic friction, which acts in the opposite direction to the motion of the box.

4. **Effect of Kinetic Friction**: When the push is stopped, the box will no longer have the force propelling it forward. The kinetic friction will now act to decelerate the box. The box will start to slow down because the frictional force is acting against its motion.

5. **Final Outcome**: As the box continues to move, the kinetic friction will gradually reduce its velocity. Eventually, the box will come to a stop when its velocity reaches zero.

Thus, the answer to the question is: If the push is stopped, the box will **slow down and eventually stop**.

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