How do you calculate kinetic energy?

Definition

Kinetic energy is the energy an object possesses due to its motion. For an object of mass $m$ moving at velocity $v$, the kinetic energy ($KE$) is given by:

$$ KE = \frac{1}{2} m v^2 $$

where:

• $KE$ = kinetic energy (in joules, J)
• $m$ = mass of the object (in kilograms, kg)
• $v$ = speed of the object (in meters per second, m/s)

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Worked Example

Question:
A ball of mass $2,text{kg}$ is moving at a speed of $3,text{m/s}$. What is its kinetic energy? **Step 1: Write the formula** %%MATH_DISPLAY_1%% **Step 2: Substitute the values** - $m = 2,text{kg}$ - $v = 3,text{m/s}$ %%MATH_DISPLAY_2%% **Step 3: Calculate $v^2$** %%MATH_DISPLAY_3%% **Step 4: Multiply** %%MATH_DISPLAY_4%% **Final Answer:** %%MATH_DISPLAY_5%% --- ## Takeaways - Kinetic energy depends on both mass and the square of velocity. - The formula is $KE = frac{1}{2} m v^2$.

• Doubling the speed will quadruple the kinetic energy.