QuestionAugust 17, 2025

Select the correct answer. A race car passes its first checkpoint at a constant speed of 20m/s and immediately begins accelerating at a rate of 10m/s^2 How long will the car take to reach the finish line 480 meters beyond the checkpoint? This problem can be represented using the following equation. ((1)/(2))10t^2+20t=480 8 seconds 16 seconds 24 seconds 12 seconds

Select the correct answer. A race car passes its first checkpoint at a constant speed of 20m/s and immediately begins accelerating at a rate of 10m/s^2 How long will the car take to reach the finish line 480 meters beyond the checkpoint? This problem can be represented using the following equation. ((1)/(2))10t^2+20t=480 8 seconds 16 seconds 24 seconds 12 seconds
Select the correct answer. A race car passes its first checkpoint at a constant speed of 20m/s and immediately begins accelerating at a rate of 10m/s^2 How long will the car take to reach the finish line 480 meters beyond the checkpoint? This problem can be represented using the following equation. ((1)/(2))10t^2+20t=480 8 seconds 16 seconds 24 seconds 12 seconds

Solution
4.5(266 votes)

Answer

8 seconds Explanation 1. Solve the quadratic equation Use the formula ax^2 + bx + c = 0. Here, a = 5, b = 20, and c = -480. Apply the quadratic formula: t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. 2. Calculate discriminant Compute b^2 - 4ac: 20^2 - 4 \cdot 5 \cdot (-480) = 400 + 9600 = 10000. 3. Find roots using quadratic formula Substitute into the formula: t = \frac{-20 \pm \sqrt{10000}}{10}. This gives t = \frac{-20 \pm 100}{10}. 4. Determine positive root Calculate t = \frac{80}{10} = 8 seconds.

Explanation

1. Solve the quadratic equation<br /> Use the formula $ax^2 + bx + c = 0$. Here, $a = 5$, $b = 20$, and $c = -480$. Apply the quadratic formula: $t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.<br />2. Calculate discriminant<br /> Compute $b^2 - 4ac$: $20^2 - 4 \cdot 5 \cdot (-480) = 400 + 9600 = 10000$.<br />3. Find roots using quadratic formula<br /> Substitute into the formula: $t = \frac{-20 \pm \sqrt{10000}}{10}$. This gives $t = \frac{-20 \pm 100}{10}$.<br />4. Determine positive root<br /> Calculate $t = \frac{80}{10} = 8$ seconds.
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