Aperson runs at a constant speed around a 100m diameter circular track and completes each lap in 60 sec. what is the magnitude of the runner's average velocity for one fourth of a lap?

1.31 m/s

Explanation:

t = 60sec

d= 100m, r = d/2 = 100/2 = 50m

distance = Circumference= 2πr = 314.2m

one fourth of a lap, d= 314.2/4 = 78.55 m

v = s/t = 78.55/60 = 1.31 m/s

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.