A 810 kg car accelerates from rest to 27 m/s in a distance of 120 m. What is the magnitude of the average net force acting on the car ?

Options

A. 740 N
B. 2500 N
C. 91 N
D. 1300 N

Answer

To find the magnitude of the average net force acting on the car, we can follow these steps:

### Step 1: Identify the given values
- Mass of the car (m) = 810 kg
- Initial velocity (u) = 0 m/s (the car starts from rest)
- Final velocity (v) = 27 m/s
- Displacement (s) = 120 m

### Step 2: Use the third equation of motion to find acceleration (a)
The third equation of motion is given by:
\[ v^2 = u^2 + 2as \]

Substituting the known values:
\[ (27)^2 = (0)^2 + 2a(120) \]

This simplifies to:
\[ 729 = 2a(120) \]

### Step 3: Solve for acceleration (a)
Rearranging the equation to isolate 'a':
\[ 729 = 240a \]
\[ a = \frac{729}{240} \]

Calculating the value:
\[ a = 3.0375 \, \text{m/s}^2 \]
For simplicity, we can round this to:
\[ a \approx 3.04 \, \text{m/s}^2 \]

### Step 4: Calculate the average net force (F_avg)
Using Newton's second law, the average net force can be calculated as:
\[ F_{avg} = m \cdot a \]

Substituting the values:
\[ F_{avg} = 810 \, \text{kg} \cdot 3.04 \, \text{m/s}^2 \]

Calculating the force:
\[ F_{avg} = 2464 \, \text{N} \]

### Final Answer
The magnitude of the average net force acting on the car is approximately **2464 N**.

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