A vehicle is moving on a rough road in a straight line with uniform velocity

Options

A. No net force is acting on vehicle
B. A net force must acting on the vehicle
C. An acceleration is being produced in the vehicle
D. An centripetal acceleration is being produced in the vehicle

Answer

To solve the problem, we need to analyze the situation of a vehicle moving on a rough road with uniform velocity. Let's break it down step by step.

### Step-by-Step Solution:

1. **Understanding the Motion**:
The vehicle is moving on a rough road in a straight line with uniform velocity. Uniform velocity means that the speed and direction of the vehicle are constant.

**Hint**: Recall that uniform velocity indicates no change in speed or direction.

2. **Identifying Forces**:
On a rough road, there is friction acting against the motion of the vehicle. The vehicle's engine provides a force to overcome this friction.

**Hint**: Consider the forces acting on the vehicle: the driving force from the engine and the frictional force.

3. **Calculating Acceleration**:
Since the vehicle is moving with uniform velocity, the acceleration is zero. Acceleration is defined as the rate of change of velocity. If the velocity is constant, then:
\[ a = \frac{dv}{dt} = 0 \]

**Hint**: Remember that acceleration is zero when there is no change in velocity.

4. **Applying Newton's Second Law**:
According to Newton's second law, the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
\[ F_{net} = m \cdot a \]
Since \( a = 0 \), we have:
\[ F_{net} = m \cdot 0 = 0 \]

**Hint**: A net force of zero means that all forces acting on the vehicle are balanced.

5. **Analyzing Forces**:
The vehicle experiences a driving force \( F_e \) from the engine and a frictional force \( f \) opposing it. For the vehicle to maintain a uniform velocity, these forces must be equal:
\[ F_e = f \]
Thus, while there are forces acting on the vehicle, they are balanced, resulting in a net force of zero.

**Hint**: Balance of forces is key to maintaining uniform motion.

6. **Evaluating Statements**:
- **Statement 1**: "No net force is acting on the vehicle." - This is true.
- **Statement 2**: "A net force must be acting on the vehicle." - This is false.
- **Statement 3**: "An acceleration is being produced in the vehicle." - This is false since acceleration is zero.
- **Statement 4**: "A centripetal acceleration is being produced in the vehicle." - This is also false as centripetal acceleration applies to circular motion, not straight-line motion.

**Hint**: Carefully evaluate each statement based on the analysis of forces and motion.

### Conclusion:
The correct statement is that no net force is acting on the vehicle. The vehicle maintains its uniform velocity due to the balance of forces.