Compute your average velocity in the following two cases: (a) You walk 85.5 m at a speed of 1.41 m/s and then run 85.5 m at a speed of 4.15 m/s along a straight track. (b) You walk for 1.00 min at a speed of 1.41 m/s and then run for 1.32 min at 4.15 m/s along a straight track.

a) The average speed was V = 2.1 m/s

b) The average speed was V = 2.97 m/s

Explanation:

The average velocity is given by the distance travelled by the time it took to travel it.

a) In this case we have two stages, both with the same length of 85.5 m so the total distance will be the sum of both that is 85.5 + 85.5 = 171 m. We are then given the speed for both stages. In order to calculate the average speed we need to compute the total time it took to complete the route, to do that we need to calculate the time it took to complete each stage. So we have:

t_1 = S1/V1 = 85.5/1.41 =  60.64 s

t_2 = S2/V2 = 85.5/4.15 = 20.60s

total time = t1 + t2 = 60.64 + 20.60 = 81.24 s

V = total length/ total time = 171/81.24 = 2.1 m/s

b) In this case we have the time it took for each stage, they're given in minutes so the first thing we need to do is convert them to seconds, we do that by multiplying it by 60. We have:

t1 = 1*60 = 60 s

t2 = 1.32*60 = 79.2 s

total time = 139.2 s

We can now compute the length of each stage, we do that by multiplying the time it took to complete each stage by the speed of each. We have:

S1 = 60*1.41 = 84.6 m

S2 = 79.2*4.15 = 328.68 m

total length = 84.6 + 328.6 = 413.28 m

V = total length / total time = 413.28 / 139.2 = 2.97 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.

the journeys of marquette, joliet and la salle a) new france expand.

all three of these explorers explored the midwest and the area around the great lakes, which they subsequently claimed for france.

this was a big portion of territory and expanded new france which before then only consisted of quebec province in northeastern canada