Asoccer player kicks a soccer ball of mass 0.45 kg that is initially at rest. the foot of the player is in contact with the ball for
3.0×10−3s
, and the force of the kick is given by
f(t)=[(6.0×106)t−(2.0×109)t²]n
for
0≤t≤3.0×10−3s
, where t is in seconds. find the magnitudes of: (a) the impulse on the ball due to the kick, (b) the average force on the ball from the player’s foot during the period of contact, (c) the maximum force on the ball from the player’s foot during the period of contact, and (d) the ball’s velocity immediately after it loses contact with the player’s foot.

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.