Kinematics position function question

In summary, the conversation is about a person studying for an AP test and needing help with a problem involving a particle's position at a given time. The equation provided is X = (t^3 - 3t^2 + 6t)m, where m is meters and t is seconds. The person has tried factoring and using the quadratic formula but has not been successful. They are specifically looking for the position of the particle at its minimum speed after t = 0.
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CuelloFactor
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< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >

I'm studying for AP test. This is not a homework question. Does anyone know how to do number 2? I don't even know where to start. I tried factoring out t and using quadratic formula, but I kept getting imaginary roots and t can't equal zero.

X = (t^3 - 3t^2 + 6t)m

where m is meters and t is seconds.
What is the position of the particle when it is at its minimum speed (after t = 0)

thanks in advance for anyone that answers.
 

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What is the kinematics position function?

The kinematics position function is a mathematical equation that describes the position of an object over time. It is typically represented as x(t), where x represents the position and t represents time. It is a fundamental concept in physics and is used to study the motion of objects.

How is the kinematics position function related to velocity and acceleration?

The kinematics position function is related to velocity and acceleration through its derivatives. The first derivative of the position function is velocity, and the second derivative is acceleration. This means that by taking the derivatives of the position function, we can determine the velocity and acceleration of an object at any given time.

How do you graph the kinematics position function?

To graph the kinematics position function, we plot the position x on the y-axis and time t on the x-axis. The resulting graph is a curve that shows the position of the object over time. The slope of the curve at any point represents the velocity, and the concavity of the curve represents the acceleration.

How can the kinematics position function be used to solve real-world problems?

The kinematics position function can be used to solve a variety of real-world problems, such as finding the distance traveled by an object, determining the velocity needed to reach a certain position, or predicting the future position of an object. It is a powerful tool for analyzing and understanding the motion of objects in the physical world.

What are the units of the kinematics position function?

The units of the kinematics position function depend on the units of the position and time variables. If the position is measured in meters and time is measured in seconds, then the units of the position function will be meters per second (m/s). It is important to pay attention to units when working with the kinematics position function to ensure accurate calculations and interpretations.

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