Given `KE=(1)/(2)mv^(2)`. If `m=10kg, v=5m//s` then find the value of KE?

Answer

To find the kinetic energy (KE) of an object, we can use the formula:

\[ KE = \frac{1}{2} mv^2 \]

Where:
- \( m \) is the mass of the object,
- \( v \) is the velocity of the object.

Given:
- \( m = 10 \, \text{kg} \)
- \( v = 5 \, \text{m/s} \)

Now, we will substitute the values of \( m \) and \( v \) into the formula.

### Step 1: Substitute the values into the formula

\[ KE = \frac{1}{2} \times 10 \, \text{kg} \times (5 \, \text{m/s})^2 \]

### Step 2: Calculate \( v^2 \)

First, calculate \( (5 \, \text{m/s})^2 \):

\[ (5 \, \text{m/s})^2 = 25 \, \text{m}^2/\text{s}^2 \]

### Step 3: Substitute \( v^2 \) back into the equation

Now substitute \( v^2 \) back into the equation:

\[ KE = \frac{1}{2} \times 10 \, \text{kg} \times 25 \, \text{m}^2/\text{s}^2 \]

### Step 4: Calculate \( \frac{1}{2} \times 10 \)

Calculate \( \frac{1}{2} \times 10 \):

\[ \frac{1}{2} \times 10 = 5 \]

### Step 5: Multiply by \( 25 \, \text{m}^2/\text{s}^2 \)

Now multiply:

\[ KE = 5 \times 25 \, \text{kg} \cdot \text{m}^2/\text{s}^2 \]

### Step 6: Calculate the final value

\[ KE = 125 \, \text{J} \]

Thus, the kinetic energy of the object is:

\[ \boxed{125 \, \text{J}} \]