The distance of feet, from a fixed piont of an object moving in a straight line is given by p=-5t^2-15t+100, where t is the time in seconds. How much time is r

Question

How much time is required for the object to travel 50 feet?  I know the answer should be 2sec. but I am missing something. please help me understand how to get that. thank you

Answer 1

p = -5t²-15t+100

 

We want p = 50 feet.  We need to solve for t, the time it takes to go 50 feet.

 

50 = -5t²-15t+100

 

0 = -5t²-15t+50         [Subtracted 50 from both sides]

 

The quadratic factors to:

 

-(5t+25)(t-2)     [You can also use the quadratic formula to solve for t]

 

t = -5 and 2

 

Can't have a negative time, so t = 2 sec

 

Check:

 

p = -5(2²) - 15(2) + 100 = -20 - 30 + 100 = 50 feet        CHECK!