Atest rocket is launched vertically from guard level (y= 0m) at time t = 0.0s. the rocket engine provides constant acceleration during the burn phase. at the instant of the engine burnout the rocket has risen to 49m and acquired a velocity of 30 m/s. how long did the burn phase last

If the rocket had zero speed at ignition and 30 m/s at burnout, and the acceleration was constant throughout the burn, then its average speed over the duration was 15 m/s .

Time = (total distance covered) / (average speed)  

Time = (49 m) / (15 m/s)

Time = 3.27 seconds

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.