Verifying: Solving Quadratic Equations for Time

In summary, the conversation discusses how to solve for the time when an object will be at a certain height using the equation x=x0+v0t+(1/2)at^2. However, since the equation is quadratic in t, there will be two answers due to the object passing through its initial displacement twice during its motion.
  • #1
savva
39
0
Could anyone please verify with me that I have the right idea in answering the question below.

Homework Statement


If you know the initial velocity v0 and the initial and final heights y0 and y, you can use x=x0+v0t+(1/2)at^2 to solve for the time t when the object will be at height y. But the equation is quadratic in t, so you'll get two answers. Physically, why is this?

The Attempt at a Solution


This occurs because during the motion of an object it has passed through it's initial displacement on 2 occassions. Thus times occur twice.
 
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  • #2
One on the way up and the other on the way down probably.
 

What is the difference between verifying and solving quadratic equations for time?

Verifying a quadratic equation for time involves substituting a specific value for time into the equation and checking if it satisfies the equation. Solving a quadratic equation for time involves finding the value or values of time that make the equation true.

Why is it important to verify solutions to quadratic equations for time?

Verifying solutions ensures that the values of time we have found actually satisfy the quadratic equation. This helps us avoid mistakes and ensures the accuracy of our solutions.

In what situations might we need to verify solutions to quadratic equations for time?

We might need to verify solutions when we are solving real-world problems that involve time. For example, if we are solving a physics problem involving motion, we would want to verify that the time values we have found make sense in the context of the problem.

What are some common methods for verifying solutions to quadratic equations for time?

One common method is to plug the time values into the equation and simplify to see if the equation is true. Another method is to graph the equation and see if the time values correspond to points on the graph.

Are there any special cases we should be aware of when verifying solutions to quadratic equations for time?

Yes, there are a few special cases to keep in mind. If the quadratic equation has imaginary solutions, we cannot verify them using real numbers. Also, if the equation has a radical in the solution, we need to make sure the time value we are verifying is in the domain of the radical.

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