# Question #5b15a

##### 1 Answer

Feb 12, 2017

The kinetic energy increases by a factor of

#### 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

#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")))#