Finding numeric values of variables A & B from an equation

Question

An amusement park designs a roller-coaster ride based on the function f(t)=at^2-bt+20, where t is the time of the ride in seconds. The designer wants to achieve the speed f'(1)=10 mph, and f'(15)=80 mph, what should the design parameters a & b be? (I'm assuming we're working with the derivative of the function f'(t)=2at-b

Answer 1

Hi Morgan

 

We have been given

f(t) = at² - bt + 20

and the first derivative is

f'(t) 2at-b

 

We also have f'(1) = 10 and f'(15) = 80

 

So evaluate the first derivative at each value of t

f'(1) = 2a-b = 10

f'(15) = 30a-b = 80

 

Subtract f'(1) from f'(15)

28a = 70

a = 5/2

 

Then use this value of a in one of the f'(t) equations and solve for b.

f'(1) = 2(5/2) - b = 10

5-b = 10

b=-5

 

 

a = 5/2

b = -5