When a constant force acts on an object with a mass of 8 kg for a duration of 3 s, it increases the object's velocity from 4 `ms^(-1)` to 6 `ms^(-1)`. What is the magnitude of the applied force?

Options

A. A) 5.33 N
B. B) 4.33 N
C. C) 6.33 N
D. D) 3.33 N

Answer

To find the magnitude of the applied force, we can follow these steps:

### Step 1: Identify the given values
- Mass of the object (m) = 8 kg
- Initial velocity (u) = 4 m/s
- Final velocity (v) = 6 m/s
- Time duration (t) = 3 s

### Step 2: Calculate the acceleration (a)
Acceleration is defined as the change in velocity over time. We can use the formula:

\[ a = \frac{v - u}{t} \]

Substituting the given values:

\[ a = \frac{6 \, \text{m/s} - 4 \, \text{m/s}}{3 \, \text{s}} = \frac{2 \, \text{m/s}}{3 \, \text{s}} = \frac{2}{3} \, \text{m/s}^2 \]

### Step 3: Use Newton's second law to find the force (F)
According to Newton's second law, the force can be calculated using the formula:

\[ F = m \cdot a \]

Substituting the values of mass and acceleration:

\[ F = 8 \, \text{kg} \cdot \frac{2}{3} \, \text{m/s}^2 \]

Calculating this gives:

\[ F = \frac{16}{3} \, \text{N} \approx 5.33 \, \text{N} \]

### Final Answer
The magnitude of the applied force is approximately **5.33 N**.

---