What force should be applied on a body of mass 500 kg to change its velocity from 4 `ms^(1)` to 6 `ms^(-1)` in one second ?

Options

A. 250 N
B. 500 N
C. 1000 N
D. 2000 N

Answer

To solve the problem of determining the force required to change the velocity of a body with a mass of 500 kg from 4 m/s to 6 m/s in one second, we can follow these steps:

### Step 1: Identify the given values
- Mass of the body (m) = 500 kg
- Initial velocity (u) = 4 m/s
- Final velocity (v) = 6 m/s
- Time (t) = 1 s

### Step 2: Calculate the change in velocity (Δv)
The change in velocity (Δv) can be calculated using the formula:
\[ \Delta v = v - u \]
Substituting the values:
\[ \Delta v = 6 \, \text{m/s} - 4 \, \text{m/s} = 2 \, \text{m/s} \]

### Step 3: Calculate the acceleration (a)
Acceleration (a) is defined as the change in velocity over time:
\[ a = \frac{\Delta v}{t} \]
Substituting the values:
\[ a = \frac{2 \, \text{m/s}}{1 \, \text{s}} = 2 \, \text{m/s}^2 \]

### Step 4: Apply Newton's second law of motion
According to Newton's second law, the force (F) applied on an object is given by:
\[ F = m \cdot a \]
Substituting the values:
\[ F = 500 \, \text{kg} \cdot 2 \, \text{m/s}^2 = 1000 \, \text{N} \]

### Conclusion
The force that should be applied on the body to change its velocity from 4 m/s to 6 m/s in one second is **1000 N**.

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