Can you solve this?

Question

1, The equation d = (1/2)at² gives the distance d in ft that an object travels 2 from rest while accelerating where a is the accerleration and t is the time .
a. How far has an object traveled in 4s when the accerleration is 5ft/s2?
b. How long does it take an object to travel 100ft when the acceleration is 8ft/s2?

2. The number of people recycling in a community is modeled by the function n = 90sqrt(3t) + 400, where t is the number of months the recycling plant has been open.
a. Find the number of people recycling when the plant has been open for 6 months.
b. Find the month when about 670 people are recycling

Answer 1

Hi Sydney,

 

1) a)

d = (1/2)at^2

d = (1/2)*5*4^2

= 40 ft

 

b) 100 = (1/2)*8*t^2

100 = 4t^2

25 = t^2

t = 5 sec

 

2)  n = 90sqrt(3t) + 400

a) n = 90sqrt(3*6) + 400

= 781 people (rounded to 781)

 

b) 670 = 90sqrt(3t) + 400

270 = 90sqrt(3t)

3 = sqrt(3t)

9 = 3t (squared both sides)

t = 3 months