In a system with only a single force acting upon a body, what is the relationship between the change in kinetic energy and the work done by the force?

Answers:

Work is equal to the change in kinetic energy.
Work depends on the square of the change in potential energy.
Work is equal to the negative of the change in kinetic energy.
Work is equal to the square of the change in kinetic energy

Work is equal to the change in kinetic energy.

Explanation:

The law relating work and kinetic energy states that "the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle."

This theorem is also called the work energy principle.

It was derived from the law of conservation of energy.

This principle stands even if there is a single force acting on the body. The change in the kinetic energy of the body is equal to the work done.

Mathematically,

W = ΔK.E.

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.