What force will change the velocity of a body of mass 1 kg from `20 ms^(-1) `to `30 ms^(-1)` in two seconds?

Options

A. 1N
B. `5N`
C. `10 N`
D. `25 N`

Explanation

To solve the problem of finding the force required to change the velocity of a body of mass 1 kg from 20 m/s to 30 m/s in 2 seconds, we can follow these steps:

### Step 1: Identify the given values
- Mass of the body (m) = 1 kg
- Initial velocity (u) = 20 m/s
- Final velocity (v) = 30 m/s
- Time (t) = 2 seconds

### Step 2: Calculate the acceleration
We can use the first equation of motion, which relates initial velocity, final velocity, acceleration, and time:
\[ v = u + at \]

Rearranging this equation to solve for acceleration (a):
\[ a = \frac{v - u}{t} \]

Substituting the known values:
\[ a = \frac{30 \, \text{m/s} - 20 \, \text{m/s}}{2 \, \text{s}} \]
\[ a = \frac{10 \, \text{m/s}}{2 \, \text{s}} \]
\[ a = 5 \, \text{m/s}^2 \]

### Step 3: Calculate the force
Using Newton's second law of motion, which states that force (F) is the product of mass (m) and acceleration (a):
\[ F = m \cdot a \]

Substituting the values we have:
\[ F = 1 \, \text{kg} \cdot 5 \, \text{m/s}^2 \]
\[ F = 5 \, \text{N} \]

### Conclusion
The force required to change the velocity of the body from 20 m/s to 30 m/s in 2 seconds is **5 Newtons**.

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