Work, Energy and Power: Question 6

Worked solution

Step 1: Recall the definition of kinetic energy

The kinetic energy of an object of mass $m$ moving at speed $v$ is: $E_k = \tfrac12mv^2$

Step 2: Substitute the values

$E_k = \tfrac12\times55\times4.0^2$

First square the speed: $4.0^2=16$. Then multiply by the mass: $55\times16=880$. Finally halve this result: $\tfrac12\times880=440\text{ J}$.

Check by recomputing in a different order: $\tfrac12\times55=27.5$, and $27.5\times16=440\text{ J}$. Both routes agree.

Why the other options are wrong

• A ($880\text{ J}$): this is $mv^2$ with the factor of $\tfrac12$ left out entirely.
• B ($110\text{ J}$): this comes from using $v$ instead of $v^2$, i.e. $\tfrac12\times55\times4.0=110\text{ J}$.
• C ($220\text{ J}$): this is the product $mv=55\times4.0=220\text{ J}$, which is not kinetic energy at all, it omits both the square and the factor of $\tfrac12$.

Final answer

• The kinetic energy of the skateboarder is $\boxed{440}\text{ J}$, option D.