Question

The car is driving down the road with a kinetic energy of 56J. What is its new kinetic energy now if its velocity is doubled?

Answer 1

The new kinetic energy is 224 J

Step-by-step explanation:

Recall that kinetic energy is defined as:
`(1)/(2) m\, v^2` where m is the mass of the object and v its velocity. So the initial situation is that the car has a kinetic energy equal to 56 J when its velocity is "v". Therefore, at this initial velocity, the kinetic energy of the car is;

`(1)/(2) m\,v^2 = 56\, J`

in the new new situation, the car has doubled its velocity: from
`v` went to
`2v`, without any change in its mass. This means that its new kinetic energy is now given by:

`Knew=(1)/(2) m\, (2v)^2=(1)/(2) m\, 4 \,v^2= 4 * ((1)/(2) m\, v^2)`

which is four times its initial kinetic energy. That is: 4 * 56 J = 224 J