The amount of kinetic energy an object has depends on its mass and its speed. Rank the following sets of oranges and cantaloupes from least kinetic energy to greatest kinetic energy. If two sets have the same amount of kinetic energy, place one on top of the other. 1. mass: m speed: v2. mass: 4 m speed: v3. total mass: 2 m speed: 1/4v4. mass: 4 m : speed: v5. total mass: 4 m speed: 1/2v

mass₃<mass₁=mass₅<mass₂=mass₄

Explanation:

Given data :-

1. mass:  m      speed: v

2. mass: 4 m   speed: v

3. mass: 2 m   speed: ¼ v

4. mass: 4 m   speed: v

5. mass: 4 m   speed: ½ v

We know that Kinetic energy (KE) = ½ mv²

Where m= mass of the body

           v=velocity of the body

Substituting the values of respective mass and velocity from the above given data-

KE of Body 1(mass₁) = ½*m*v²             = mv²/2

KE of Body 2(mass₂) = ½*4m*v²         = 2mv²

KE of Body 3(mass₃) = ½*2m*(1/4v)²  =  mv²/16

KE of Body 4(mass₄) = ½*4m*v ²        =  2mv ²

KE of Body 5(mass₅) = ½*4m*(1/2v)²  =   mv²/2

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.