A vehicle of mass 20kg is moving with a velocity of `4 ms^(-1)`. Find the magnitude of the force that is to be applied on the vehicle so that the vehicle have a velocity of `1 ms^(-1)` after travelling a distance of 20m.

Options

A. 4 N
B. 6 N
C. 7.5 N
D. 9.5 N

Answer

To solve the problem, we will use the equations of motion and Newton's second law. Here are the steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Mass of the vehicle (m) = 20 kg
- Initial velocity (u) = 4 m/s
- Final velocity (v) = 1 m/s
- Distance (s) = 20 m

2. **Use the third equation of motion:**
The third equation of motion relates initial velocity, final velocity, acceleration, and distance:
\[ v^2 = u^2 + 2as \]
where \( a \) is the acceleration.

3. **Substitute the known values into the equation:**
\[ (1)^2 = (4)^2 + 2a(20) \]
This simplifies to:
\[ 1 = 16 + 40a \]

4. **Rearrange the equation to solve for acceleration (a):**
\[ 40a = 1 - 16 \]
\[ 40a = -15 \]
\[ a = \frac{-15}{40} = -0.375 \, \text{m/s}^2 \]

5. **Use Newton's second law to find the force (F):**
According to Newton's second law:
\[ F = ma \]
Substituting the values we have:
\[ F = 20 \times (-0.375) \]
\[ F = -7.5 \, \text{N} \]

6. **Determine the magnitude of the force:**
The magnitude of the force is:
\[ |F| = 7.5 \, \text{N} \]

### Final Answer:
The magnitude of the force that is to be applied on the vehicle is **7.5 N**.

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