Which pair of graphs represent the same motion of an object

The pair of graphs that represent the same motion of an object is ; ( D )

Given that :

Velocity = displacement / time

From the equation :

   Velocity is directly  proportional to displacement when time is kept constant . therefore increase in displacement will lead to an increase in velocity of an object.

   Meanwhile when time varies ( change in time ) and an object moves at a constant velocity there will  be an increase in displacement.

  Hence we can conclude that the pair of graphs that represents the same motion of an object is graph D  

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hypothesising or postulating

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.