A car is travelling at a velocity of 10 m/s and has a mass of 850 kg. What is its kinetic energy?

Answer

To find the kinetic energy of the car, we will use the formula for kinetic energy (KE):

### Step 1: Write down the formula for kinetic energy.
The formula for kinetic energy is given by:
\[ KE = \frac{1}{2} mv^2 \]
where:
- \( m \) is the mass of the object (in kilograms),
- \( v \) is the velocity of the object (in meters per second).

### Step 2: Identify the values given in the problem.
From the question, we have:
- Mass of the car, \( m = 850 \, \text{kg} \)
- Velocity of the car, \( v = 10 \, \text{m/s} \)

### Step 3: Substitute the values into the formula.
Now, we substitute the values of mass and velocity into the kinetic energy formula:
\[ KE = \frac{1}{2} \times 850 \, \text{kg} \times (10 \, \text{m/s})^2 \]

### Step 4: Calculate \( v^2 \).
First, calculate \( (10 \, \text{m/s})^2 \):
\[ (10 \, \text{m/s})^2 = 100 \, \text{m}^2/\text{s}^2 \]

### Step 5: Substitute \( v^2 \) back into the formula.
Now substitute \( v^2 \) back into the kinetic energy formula:
\[ KE = \frac{1}{2} \times 850 \, \text{kg} \times 100 \, \text{m}^2/\text{s}^2 \]

### Step 6: Calculate \( \frac{1}{2} \times 850 \).
Calculate \( \frac{1}{2} \times 850 \):
\[ \frac{1}{2} \times 850 = 425 \, \text{kg} \]

### Step 7: Multiply by \( 100 \).
Now multiply \( 425 \, \text{kg} \) by \( 100 \, \text{m}^2/\text{s}^2 \):
\[ KE = 425 \, \text{kg} \times 100 \, \text{m}^2/\text{s}^2 = 42500 \, \text{kg m}^2/\text{s}^2 \]

### Step 8: Convert to Joules.
Since \( 1 \, \text{kg m}^2/\text{s}^2 = 1 \, \text{Joule} \), we have:
\[ KE = 42500 \, \text{J} \]

### Step 9: Convert Joules to kilojoules.
To convert Joules to kilojoules, divide by 1000:
\[ KE = \frac{42500 \, \text{J}}{1000} = 42.5 \, \text{kJ} \]

### Final Answer:
The kinetic energy of the car is \( 42500 \, \text{J} \) or \( 42.5 \, \text{kJ} \).

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