Car's Kinetic Energy After Doubling Linear Momentum

[XwakeriderX]

The kinetic energy of a car moving down a road is 1.00 x 10^5 J. The car suddenly doubles the magnitude of it's linear momentum vector without changing it's mass. What is the new value of the car's energy?
A) 9.00 x 10^5 J
B) 4.00 x 10^5 J
C) 6.00 x 10^5 J
D) 9.00 x 10^6 J
E) none of the above!

P_>=mv_>

I thought ke was a scalar and momentum was a vector. Can this problem be done?

 

[Delphi51]

Yes, it can be done.
Are you familiar with the trick of seeing immediately that
when E = ½mv², then
- doubling m causes E to double
- doubling v causes E to quadruple
One way to see it is to replace v with (2v) and write the 2 in red;
you see that (2v)² is 4v² so the ½mv² has changed to 4(½mv²).

That is the technique to deal with your question.
You have p = mv so v = p/m
Ask yourself how doubling p affects v.
Then how that affects KE.