A trailer of mass 1000 kg is towed by means of a rope attached to a car moving at a steady speed along a level road. The tension in the rope is 400 N. The car starts to accelerate steadily. If the tension in the rope is now 1650N, with what acceleration is the trailer moving?

Options

A. `1.75ms^(-2)`
B. `0.75ms^(-2)`
C. `2.5ms^(-2)`
D. `1.25ms^(-2)`

Explanation

To solve the problem, we need to determine the acceleration of the trailer when the tension in the rope is 1650 N. We will use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of the trailer (m) = 1000 kg
- Tension in the rope (T) = 1650 N

2. **Understand the Forces Acting on the Trailer:**
- The tension in the rope is the force that pulls the trailer forward.
- There is also a frictional force acting in the opposite direction, which we need to determine.

3. **Calculate the Net Force Acting on the Trailer:**
- The net force (F_net) acting on the trailer can be calculated using the equation:
\[ F_{\text{net}} = T - F_{\text{friction}} \]
- Initially, when the tension was 400 N and the trailer was moving at a constant speed, the frictional force was equal to the tension, which means:
\[ F_{\text{friction}} = 400 \, \text{N} \]

4. **Substitute the Values into the Net Force Equation:**
- Now, substituting the values when the tension is 1650 N:
\[ F_{\text{net}} = 1650 \, \text{N} - 400 \, \text{N} = 1250 \, \text{N} \]

5. **Apply Newton's Second Law to Find the Acceleration:**
- According to Newton's second law:
\[ F_{\text{net}} = m \cdot a \]
- Rearranging for acceleration (a):
\[ a = \frac{F_{\text{net}}}{m} = \frac{1250 \, \text{N}}{1000 \, \text{kg}} = 1.25 \, \text{m/s}^2 \]

6. **Conclusion:**
- The acceleration of the trailer when the tension in the rope is 1650 N is \(1.25 \, \text{m/s}^2\).