A race car driving under the caution flag at 40 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 30t2 + 40t, where t is the time in seconds after the car starts accelerating again. How long will the car take to travel 150 feet?

t = 1.667 s

Step-by-step explanation

The distance traveled since the warning flag in feet is characterized by

d = 30*t^2 + 40*t

Where t is the time in seconds after the car starts accelerating.

We can easily solve this question by plotting the equation using a graphing calculator or plotting tool.

We need to find the time for which the distance d = 150 ft

150 = 30*t^2 + 40*t, t > = 0

We can see that this value in the graph is approximately

t = 1.667 s

We can verify

30 * (1.667) ^2 + 40 * (1.667) ≈ 150