There's a part A and b

Question

A rock is thrown down from the top of a 500 foot cliff. after 1 second the rock is traveling 45, after 3 its traveling 108 feet per secon. 

A. Assume the relationship between time, t, and speed, s, is linear and write an equation describing this relationship. Use ordered pairs of the form (t, s) 

B. Use this equation to determine the speed of the rock 5 seconds after it is dropped

Answer 1

Tabitha, we need to find the slope.

 

(108 - 45)/(3 - 1) = 63/2 = 31.5

 

Now, let's find the y-intercept.

 

108 = 31.5(3) + b

108 = 94.5 + b

b = 13.5

 

s = 31.5t + 13.5

 

s = 31.5(5) + 13.5 = 157.5 + 13.5 = 171 ft/s