Question

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?

Answer 1

To find the time it takes for the car to travel 150 feet at a constant rate of acceleration, we need to solve the equation 30t^2 + 40t = 150 for t. The car will take approximately 1.25 seconds to travel 150 feet.

Step-by-step explanation:

To find the time it takes for the car to travel 150 feet, we need to solve the equation 30t^2 + 40t = 150 for t.

First, let's set the equation equal to 0: 30t^2 + 40t - 150 = 0

Using the quadratic formula: t = (-40 ± √(40^2 - 4 * 30 * -150)) / (2 * 30)

Simplifying, we get two possible solutions: t ≈ 1.25s and t ≈ -3s. Since time can't be negative, the car will take approximately 1.25 seconds to travel 150 feet.