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The position function x(t) of a particle moving along an x axis is x = 6.00 - 6.00 t^2, with x in...

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The position function {eq}x(t) {/eq} of a particle moving along an {eq}x {/eq} axis is {eq}x = 6.00 - 6.00 t^2 {/eq}, with {eq}x {/eq} in meters and {eq}t {/eq} in seconds.

(a) At what time and

(b) where does the particle (momentarily) stop?

At what

(c) negative time and

(d) positive time does the particle pass through the origin?

Motion in one dimension

Motion in one dimension or in a straight line can be described in the following formula:

$$x(t) = x_o + v_o + \frac{1}{2}at^{2} $$

Where:

  • {eq}x{/eq} is your position at any given time
  • {eq}x_o{/eq} is your initial position
  • {eq}v_o{/eq} is your initial velocity
  • {eq}a{/eq} is your acceleration
  • {eq}t{/eq} is your time

Answer and Explanation: 1

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Given the position function

{eq}x(t) = 6.00 - 6.00t^{2} {/eq}

a) At what time does it momentarily stops

We take th first derivative with respect...

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How to Solve Uniform Motion Problems

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Chapter 10 / Lesson 5
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Uniform motion problems use words to describe objects at consistent speeds, and can be easily translated into equations of distance, rate, and time. Practice the formula in the example problems, and watch out for features in problems that add complexity.


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