The kinetic energy of a body of mass 4 kg and momentum 6 N-s will be

Options

A. 4.5 J
B. 2.5 J
C. 5.5 J
D. 3.5 J

Explanation

To find the kinetic energy of a body given its mass and momentum, we can use the relationship between momentum (P), mass (m), and kinetic energy (KE).

**Step 1: Identify the given values.**
- Mass (m) = 4 kg
- Momentum (P) = 6 N-s (which is equivalent to kg·m/s)

**Step 2: Use the formula for kinetic energy in terms of momentum.**
The formula for kinetic energy (KE) in terms of momentum (P) and mass (m) is:
\[ KE = \frac{P^2}{2m} \]

**Step 3: Substitute the values into the formula.**
Now, substitute the values of momentum and mass into the formula:
\[ KE = \frac{(6 \, \text{N-s})^2}{2 \times 4 \, \text{kg}} \]

**Step 4: Calculate the square of momentum.**
Calculate \( P^2 \):
\[ P^2 = 6^2 = 36 \, \text{N-s}^2 \]

**Step 5: Calculate the denominator.**
Calculate \( 2m \):
\[ 2m = 2 \times 4 = 8 \, \text{kg} \]

**Step 6: Substitute and simplify.**
Now substitute these values back into the kinetic energy formula:
\[ KE = \frac{36}{8} \]

**Step 7: Perform the division.**
Calculate the final value:
\[ KE = 4.5 \, \text{J} \]

Thus, the kinetic energy of the body is **4.5 joules**.