The momentum of a body is numerically equal to its kinetic energy. What is the velocity of the body in m/s?

Options

A. 2m/s
B. 3m/s
C. 4m/s
D. 1m/s

Explanation

To solve the problem where the momentum of a body is numerically equal to its kinetic energy, we will follow these steps:

### Step 1: Write the formulas for momentum and kinetic energy.
- The momentum \( p \) of a body is given by the formula:
\[ p = mv \]
where \( m \) is the mass of the body and \( v \) is its velocity.

- The kinetic energy \( KE \) of a body is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]

### Step 2: Set the momentum equal to the kinetic energy.
According to the problem, the momentum is numerically equal to the kinetic energy:
\[ p = KE \]
Thus, we can write:
\[ mv = \frac{1}{2} mv^2 \]

### Step 3: Simplify the equation.
We can cancel \( m \) from both sides of the equation, assuming \( m \neq 0 \):
\[ v = \frac{1}{2} v^2 \]

### Step 4: Rearrange the equation.
To solve for \( v \), we can rearrange the equation:
\[ v^2 - 2v = 0 \]

### Step 5: Factor the equation.
Factoring out \( v \) gives us:
\[ v(v - 2) = 0 \]

### Step 6: Solve for \( v \).
Setting each factor to zero gives us:
1. \( v = 0 \)
2. \( v - 2 = 0 \) which simplifies to \( v = 2 \)

Since we are looking for a positive velocity, we take:
\[ v = 2 \, \text{m/s} \]

### Final Answer:
The velocity of the body is \( 2 \, \text{m/s} \).

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