Question

The kinetic energy, K, of an object varies jointly with the mass of the object and the square of the velocity of the object. A 50-kg object moving at a velocity of 20 meters per second has 10,000 joules of kinetic energy. How many joules of kinetic energy does a 25-kg object moving at a velocity of 10 meters per second have?

Answer 1

The answer would be

B) 1,250 joules

Answer 2

Kinetic energy of the object = 1250 Joule.

Explanation:

Since Kinetic energy K of an object varies with the mass m and velocity v then the relation will be defined as k is directly proportional to m×v²

Therefore K = a×m×v² defines the relation

where a is a constant.

Now an object is having m = 50 kg

v = 20 meters/second

K = 10000 joules

Then from the K = a × m × v²

10000 = a×50×(20)²

a = 10000/(50×400) = 10000/20000 = 1/2

Now we know actual relation is K = (1/2)mv²

If an object is having m = 25kg

v = 10 meters/sec

Then K = (1/2)×25×(10)² = 2500/2 = 1250 joule

Therefore kinetic energy of this object will be 1250 joule.