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The equation given for the speed of the car is \( s(t) = 2t^2 \), where \( s(t) \) represents the speed of the car as a function of time \( t \) in seconds. You are asked to find how long it will take for the speed to exceed 65 mph.

We need to solve for \( t \) when \( s(t) > 65 \) mph.

1. Set the equation \( s(t) = 2t^2 \) equal to 65:
   \[
   2t^2 = 65
   \]

2. Solve for \( t \):
   \[
   t^2 = \frac{65}{2} = 32.5
   \]
   \[
   t = \sqrt{32.5} \approx 5.7 \, \text{seconds}
   \]

Thus, it will take approximately **6 seconds** for the car to exceed 65 mph.

Would you like further clarification on any part of the solution?

Here are 5 related questions to consider:
1. What happens if the speed equation changes to \( s(t) = 3t^2 \)?
2. How would you interpret the speed if the equation involved both linear and quadratic terms?
3. How can we find the acceleration from this equation?
4. What if the speed limit was 100 mph? How would that change the time required?
5. Can this equation \( s(t) = 2t^2 \) be used for negative time values?

**Tip:** Always check if units are consistent when solving word problems—speed in mph, time in seconds, etc.

If the speed of a car with a turbo engine can be modeled as a function of time using the parabolic equation s(t) = 2t^2, how many seconds will it take the car to exceed 65 mph?

Learn how to solve the quadratic equation s(t) = 2t^2 to find out how long it takes a car to exceed 65 mph. This problem covers key concepts like quadratic equations and inequalities, perfect for students in Grades 8-10.

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