Finding Joules with Kinetic energy

Question

The kinetic energy K of a moving object varies jointly with its mass M and the square of the velocity V. If an object weighing 11 kilograms and moving with a velocity of 10 meters per sechas a kinetic energy of 550 Joules, find its kinetic energy when the velocity is 25 meters per sec.

Answer 1

This is a classic case of a problem throwing a bunch of information at you to make you think it is more difficult than it actually is.  The whole phrase about the 550 Joules is needless, except that it tells you the object's mass.  To calculate kinetic energy, as you indicated in the first sentence, all you need to know is mass and speed.  So once you know mass = 11 kg and the speed in question is 25 m/s, you just go right to K = ½mv² = ½(11 kg)(25 m/s)² = 3437.5 J.