A force of 200 N is required to push a car of mass 1000 kg slowly at a constant speed along a level road. If a force of 700 N is applied, then the acceleration of the car will be

Options

A. zero
B. `0.2 m//s^2`
C. `0.5 m//s^2`
D. `1.0 m//s^2`

Explanation

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Forces Acting on the Car
When the car is being pushed at a constant speed with a force of 200 N, this force is equal to the frictional force acting against it. Therefore, the frictional force (F_friction) is 200 N.

### Step 2: Identify the Total Force Applied
When a force of 700 N is applied to the car, we need to determine the net force acting on the car that will cause it to accelerate.

### Step 3: Calculate the Net Force
The net force (F_net) acting on the car when a force of 700 N is applied can be calculated as follows:
\[ F_{\text{net}} = F_{\text{applied}} - F_{\text{friction}} \]
Where:
- \( F_{\text{applied}} = 700 \, \text{N} \)
- \( F_{\text{friction}} = 200 \, \text{N} \)

Substituting the values:
\[ F_{\text{net}} = 700 \, \text{N} - 200 \, \text{N} = 500 \, \text{N} \]

### Step 4: Apply Newton's Second Law
According to Newton's second law, the relationship between force, mass, and acceleration is given by:
\[ F_{\text{net}} = m \cdot a \]
Where:
- \( F_{\text{net}} = 500 \, \text{N} \)
- \( m = 1000 \, \text{kg} \)
- \( a = ? \) (acceleration)

### Step 5: Solve for Acceleration
Rearranging the equation to solve for acceleration (a):
\[ a = \frac{F_{\text{net}}}{m} \]
Substituting the known values:
\[ a = \frac{500 \, \text{N}}{1000 \, \text{kg}} \]
Calculating the acceleration:
\[ a = 0.5 \, \text{m/s}^2 \]

### Final Answer
The acceleration of the car when a force of 700 N is applied is:
\[ a = 0.5 \, \text{m/s}^2 \]

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