A particle of mass `0.2 kg` is moving in one dimension under a force that delivers constant power `0.5 W` to the particle.If the initial speed =0 then the final speed (in `ms^(-1)`) after `5s` is.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Calculate the Work Done
The work done (W) by the force can be calculated using the formula:
\[ W = P \times t \]
where:
- \( P \) is the power delivered to the particle (0.5 W),
- \( t \) is the time duration (5 s).

Substituting the values:
\[ W = 0.5 \, \text{W} \times 5 \, \text{s} = 2.5 \, \text{J} \]

### Step 2: Apply the Work-Energy Theorem
According to the work-energy theorem, the work done on the particle is equal to the change in kinetic energy (KE):
\[ W = \Delta KE \]
Since the initial speed is 0, the initial kinetic energy (KE_initial) is:
\[ KE_{\text{initial}} = 0 \]

Thus, the final kinetic energy (KE_final) is:
\[ KE_{\text{final}} = W = 2.5 \, \text{J} \]

### Step 3: Write the Kinetic Energy Formula
The kinetic energy of a particle is given by:
\[ KE = \frac{1}{2} m v^2 \]
where:
- \( m \) is the mass of the particle (0.2 kg),
- \( v \) is the final speed we want to find.

### Step 4: Set Up the Equation
From the previous steps, we have:
\[ 2.5 \, \text{J} = \frac{1}{2} \times 0.2 \, \text{kg} \times v^2 \]

### Step 5: Solve for Final Speed
Rearranging the equation to solve for \( v^2 \):
\[ 2.5 = 0.1 v^2 \]
\[ v^2 = \frac{2.5}{0.1} = 25 \]

Now, taking the square root to find \( v \):
\[ v = \sqrt{25} = 5 \, \text{m/s} \]

### Final Answer
The final speed of the particle after 5 seconds is:
\[ v = 5 \, \text{m/s} \]

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