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")))#