Certain force acting on a 20 kg mass changes its velocity from `5m//s to 2m//s`. calculate the work done by the force.

Explanation

To solve the problem of calculating the work done by the force acting on a 20 kg mass that changes its velocity from 5 m/s to 2 m/s, we can follow these steps:

### Step 1: Identify the given values
- Mass (m) = 20 kg
- Initial velocity (u) = 5 m/s
- Final velocity (v) = 2 m/s

### Step 2: Calculate the initial kinetic energy (KE_initial)
The formula for kinetic energy is given by:
\[ KE = \frac{1}{2} m v^2 \]
Using the initial velocity (u = 5 m/s):
\[ KE_{\text{initial}} = \frac{1}{2} \times 20 \, \text{kg} \times (5 \, \text{m/s})^2 \]
\[ KE_{\text{initial}} = \frac{1}{2} \times 20 \times 25 = 250 \, \text{J} \]

### Step 3: Calculate the final kinetic energy (KE_final)
Using the final velocity (v = 2 m/s):
\[ KE_{\text{final}} = \frac{1}{2} \times 20 \, \text{kg} \times (2 \, \text{m/s})^2 \]
\[ KE_{\text{final}} = \frac{1}{2} \times 20 \times 4 = 40 \, \text{J} \]

### Step 4: Calculate the work done by the force
The work done (W) by the force is the change in kinetic energy, which can be calculated as:
\[ W = KE_{\text{initial}} - KE_{\text{final}} \]
Substituting the values we calculated:
\[ W = 250 \, \text{J} - 40 \, \text{J} = 210 \, \text{J} \]

### Final Answer
The work done by the force is **210 Joules**.

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