Particle moving along a parabola

[Peppino]

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

A particle movies along a parabola with the displacement equation s = 0.5t².
(a graph is shown)

::::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_x² + V_y²), and V = t, I found that the y - component is √(t²-C²t²).
iii) Since the acceleration is constant, is the y-component simply C?


:::Part II::::

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

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!

 

[Peppino]

Some help would be greatly appreciated!

 

[ehild]

We need some explanation. What is s? I do not see the graph.

ehild

 

[Peppino]

I stated in the problem that the graph is s = 0.5t².

If you wish to visualize it, you may use an online graphing calculator and graph the function y = 0.5x²

http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

 

[Ratpigeon]

For part (i) - you are right,
For part (ii) you have used s_x instead of V_x to determine V_y
For part (iii) - yes, the acceleration is constant, but it is not equal to C; but maybe try determining the total acceleration, and the acceleration in the x direction instead of differentiating...
- if you typo'd s=Ct; and it's actually V_x=Ct, then your answer to part (i) is wrong, part (ii) is right and you still need to determine part (iii) - it's a constant still, but not C

For part (II)
there isn't enoguh information - is the total motion of the particle still given by s=.5t^2?
Because in that case, the particles speed can't be constant - it's speed is, as you said, is equal to t, which is a variable.
Was there any other information?

 

[ehild]

s=0.5t^2 is a scalar equation. If s is displacement, the particle moves along a straight line, not along a parabola. If a particle moves along a parabola, you need to give the relation between its coordinates. Can you show the original text of the problem?

ehild