Consider the following equations of motion.
v = v0 + at
îx = v0t + 1/2at^2
v2 = v02 + 2aîx

a. can the equations above be used in a situation where the acceleration varies with time?
b. can they be used when the acceleration is zero?

A) No, the equations presented above are the product of the derivation of position and velocity when the acceleration is constant.

The equations change to polynomial function of the second degree for the description of the acceleration when described as a function of time.

B) Yes, when the acceleration is zero it is concluded that the velocity is constant, therefore they could be used to describe the position as a function of the change in velocity.

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.