A race car driving under the caution flag at 80 feet per second begins to accelerate at a constant rate after the warning flag. The distance traveled since the warning flag in feet is characterized by 30t 2 + 80t, where t is the time in seconds after the car starts accelerating again. How long does it take the car to travel 30 feet after it begins accelerating?

Question

Nathaniel Hogan

Mathematics

18 July, 21:26

A race car driving under the caution flag at 80 feet per second begins to accelerate at a constant rate after the warning flag. The distance traveled since the warning flag in feet is characterized by 30t 2 + 80t, where t is the time in seconds after the car starts accelerating again. How long does it take the car to travel 30 feet after it begins accelerating?

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Answers (1)

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Mckenzie Burnett · Answer 1

Answer: 1/3 sec or 0.333 sec

Step-by-step explanation:

d = 30*t^2 + 80*t = 30

putting into quadratic form, a*t^2 + b*t + c = 0

30*t^2 + 80*t - 30 = 0 where: a = 30 b = 80 c = - 30

solve quadratic:

t = [-b + sqrt (b^2 - 4*a*c) ]/2*a

substitute in values above

therefore, t = 1/3 sec or 0.333 sec