Question

(a) If an object's speed is multiplied by 3, what is its kinetic energy multiplied by?(b) If an object's kinetic energy is multiplied by 4, what is its speed multiplied by?(c) If an object's kinetic energy is multiplied by 6, what is its speed multiplied by?

Answer 1

We are asked about the kinetic energy of an object. The kinetic energy is given by the following formula:

`E_k=(1)/(2)mv^2`

Where:

`\begin{gathered} m=\text{ mass} \\ v=\text{ velocity} \end{gathered}`

Part a) If the velocity is multiplied by 3 we have:

`E_k=(1)/(2)m(3v)^2`

Solving the square we get:

`E_k=(1)/(2)m9v^2`

Factoring out the 4 we get:

`E_k=9((1)/(2)mv^2)`

Therefore, the kinetic energy is multiplied by 9.

Part b) If the kinetic energy is multiplied by 4 we have in the formula:

`E_k=4((1)/(2)mv^2)`

We can move the 4 next to the velocity:

`E_k=(1)/(2)m4v^2`

Now, by properties of exponents, we can rewrite the formula as:

`E_k=(1)/(2)m(2v)^2`

Therefore, the velocity is multiplied by 2.

Part c can be solved using the same procedure as in par b.