Under which of the following conditions is the magnitude of the average velocity of a particle moving in one dimension smaller than the average speed over some time interval?

A particle moves in the +x direction and then reverses the direction of its velocity

Explanation:

This is illustrated in that when a particle moves in a straight route with no alterations in direction, this will lead to displacement and distance being equal at any point in time during the movement. Thereby the quantity of average speed and average velocity will equal.

On the other hand, should the particle reverses direction, the distance traveled will be greater than it's displacement, thereby, the average speed will be greater than the average velocity.

a and b sometimes have a positive value

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.