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Can someone please check that everything I have done so far is correct?

A particle movies along a parabola with the displacement equation s = 0.5t

(a graph is shown)

Suppose x-component is s = Ct

i) indicate direction of velocity vector and acceleration at point R (arbitrary point on graph)

ii) Determine y-component of particles velocity

iii) Determine y-component of particles acceleration

i) I suppose the velocity vector would be tangential to the graph and the acceleration vector would be parallel with the y-axis?

ii) since V = √(V

iii) Since the acceleration is constant, is the y-component simply C?

Suppose instead that the x-component of the velocity is given by [tex]\frac{C}{\sqrt{1 + t^{2}}}[/tex]

i) Show that the particle's speed is constant

I am unsure how to attempt Part II.

If you are able to answer or confirm my answers to any part of this question, thank you very much!

A particle movies along a parabola with the displacement equation s = 0.5t

^{2}.(a graph is shown)

::::Part I::::::::Part I::::

Suppose x-component is s = Ct

i) indicate direction of velocity vector and acceleration at point R (arbitrary point on graph)

ii) Determine y-component of particles velocity

iii) Determine y-component of particles acceleration

**Answers:**

i) I suppose the velocity vector would be tangential to the graph and the acceleration vector would be parallel with the y-axis?

ii) since V = √(V

_{x}^{2}+ V_{y}^{2}), and V = t, I found that the y - component is √(t^{2}-C^{2}t^{2}).iii) Since the acceleration is constant, is the y-component simply C?

:::Part II:::::::Part II::::

Suppose instead that the x-component of the velocity is given by [tex]\frac{C}{\sqrt{1 + t^{2}}}[/tex]

i) Show that the particle's speed is constant

I am unsure how to attempt Part II.

If you are able to answer or confirm my answers to any part of this question, thank you very much!

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