Question

A body of mass \(10\,\text{kg}\) is moving with a velocity of \(20\,\text{m/s}\). What is the kinetic energy?

• A. \(1000\,\text{J}\)
• B. \(2000\,\text{J}\)
• C. \(4000\,\text{J}\)
• D. \(500\,\text{J}\)

Hint:

Kinetic energy increases with the square of velocity. Doubling the velocity makes the kinetic energy four times larger.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The goal is to calculate the energy associated with the motion of a body, given its mass and constant velocity.
Step 2: Key Formula or Approach:
Kinetic Energy (\(K.E.\)) is calculated using the formula:
\[ K.E. = \frac{1}{2}mv^2 \]
where \(m\) is the mass in kg and \(v\) is the velocity in m/s.
Step 3: Detailed Explanation:
Plug the given values (\(m = 10\,\text{kg}\) and \(v = 20\,\text{m/s}\)) into the formula:
\[ K.E. = \frac{1}{2} \times 10 \times (20)^2 \]
First, square the velocity:
\[ (20)^2 = 400 \]
Now, multiply by mass and divide by 2:
\[ K.E. = 5 \times 400 \]
\[ K.E. = 2000\,\text{J} \]
Step 4: Final Answer:
The kinetic energy of the moving body is \(2000\,\text{J}\).