An army vehicle of mass 1000 kg is moving with a velocity of `10 m//s` and is acted upon by a forward force of 1000 N due to the engine and a retarding force of 500 N due to friction. What will be its velocity after 10 s

Options

A. `5m//s`
B. `10m//s`
C. `15m//s`
D. `20m//s`

Answer

To solve the problem step-by-step, we will follow these steps:

### Step 1: Identify the given values
- Mass of the vehicle, \( m = 1000 \, \text{kg} \)
- Initial velocity, \( u = 10 \, \text{m/s} \)
- Forward force due to the engine, \( F_{\text{forward}} = 1000 \, \text{N} \)
- Retarding force due to friction, \( F_{\text{friction}} = 500 \, \text{N} \)
- Time, \( t = 10 \, \text{s} \)

### Step 2: Calculate the net force acting on the vehicle
The net force \( F_{\text{net}} \) can be calculated by subtracting the retarding force from the forward force:
\[ F_{\text{net}} = F_{\text{forward}} - F_{\text{friction}} = 1000 \, \text{N} - 500 \, \text{N} = 500 \, \text{N} \]

### Step 3: Calculate the acceleration of the vehicle
Using Newton's second law, \( F = m \cdot a \), we can find the acceleration \( a \):
\[ a = \frac{F_{\text{net}}}{m} = \frac{500 \, \text{N}}{1000 \, \text{kg}} = 0.5 \, \text{m/s}^2 \]

### Step 4: Use the kinematic equation to find the final velocity
We will use the first equation of motion:
\[ v = u + a \cdot t \]
Substituting the known values:
\[ v = 10 \, \text{m/s} + (0.5 \, \text{m/s}^2 \cdot 10 \, \text{s}) \]
\[ v = 10 \, \text{m/s} + 5 \, \text{m/s} = 15 \, \text{m/s} \]

### Conclusion
The final velocity of the vehicle after 10 seconds is \( 15 \, \text{m/s} \).

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