A moving body of 40 kg has 180 J of KE. Calculate the speed.

Answer

To solve the problem of finding the speed of a moving body with a given mass and kinetic energy, we can follow these steps:

### Step 1: Write down the formula for kinetic energy.
The formula for kinetic energy (KE) is given by:
\[ KE = \frac{1}{2} m v^2 \]
where:
- \( KE \) is the kinetic energy,
- \( m \) is the mass of the body,
- \( v \) is the speed of the body.

### Step 2: Identify the given values.
From the question, we have:
- Mass \( m = 40 \) kg,
- Kinetic Energy \( KE = 180 \) J.

### Step 3: Substitute the known values into the kinetic energy formula.
Substituting the values into the formula:
\[ 180 = \frac{1}{2} \times 40 \times v^2 \]

### Step 4: Simplify the equation.
First, calculate \( \frac{1}{2} \times 40 \):
\[ \frac{1}{2} \times 40 = 20 \]
So, the equation becomes:
\[ 180 = 20 v^2 \]

### Step 5: Solve for \( v^2 \).
To isolate \( v^2 \), divide both sides by 20:
\[ v^2 = \frac{180}{20} \]
Calculating the right side gives:
\[ v^2 = 9 \]

### Step 6: Take the square root to find \( v \).
Now, take the square root of both sides:
\[ v = \sqrt{9} \]
Thus, we find:
\[ v = 3 \text{ m/s} \]

### Final Answer:
The speed of the moving body is \( 3 \text{ m/s} \).

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