Question

Question #5b15a

Answer 1

The kinetic energy increases by a factor of `4`.

Explanation:

As you know, the kinetic energy of an object is given by the equation

`color(blue)(ul(color(black)(K_"E" = 1/2 * m* v^2)))`

Here

• `m` is the mass of the object
• `v` is its velocity

This equation shows that the kinetic energy of an object varies with the square of its velocity.

Let's say that you have

`K_"E 1" = 1/2 * m* v_1^2`

If you double the object's velocity

`v_2 = 2 * v_1`

then its kinetic energy will increase by a factor of `4`, since

`K_"E 2" = 1/2 * m * v_2^2`

`K_"E 2" = 1/2 * m * (2 * v_1)^2`

`K_"E 2" = 1/2 * m * v_1^2 * 2^2`

But since

`K_"E 1" = 1/2 * m * v_1^2`

you can say that

`K_"E 2" = K_"E 1" * 2^2`

which is equivalent to

`color(darkgreen)(ul(color(black)(K_"E 2" = 4 * K_"E 1")))`