vel/acc question (2 Viewers)

[aphorae]

Okay I suck at these questions, can someone explain to me HSC 1998 6bii)? I don't get the Success One solution (and it doesn't follow the marker's comments for full marks) and the Maths Association one involves testing points and sketching a full on diagram which seems a bit ridiculous to me for 2 marks.

http://i54.tinypic.com/33m3g5w.jpg

Marker's comments:

The candidates were asked to decide, with justification, whether or not the particle returned to the origin. To score full marks, the candidates had to refer to the expressions for acceleration and velocity and explain that the particle comes to rest and returns towards the origin. The best answers showed that v^2 does not again become zero, but not all successful candidates managed to do this. One mark was awarded to candidates for a meaningful partial explanation.

This part was badly done, with hardly any candidates showing enough understanding of the movement of the particle to score full marks. A small number were able to score one mark. Very few understood the implications of the signs of acceleration and velocity, and confusion between negative acceleration and negative velocity was common. Many candidates thought that this question was about simple harmonic motion, and gave simplistic arguments to support their conclusion based solely on whether or not they thought that the particle executed simple harmonic motion.

It is clear from the responses to this question that candidates are quite happy to deal with motion questions on a formal level, but very few are able to conceptualise what the motion is actually all about.

How do I show the particle comes to rest and returns towards the origin...? + the v^2 does not become 0 part?

 

[cssftw]

Okay I suck at these questions, can someone explain to me HSC 1998 6bii)? I don't get the Success One solution (and it doesn't follow the marker's comments for full marks) and the Maths Association one involves testing points and sketching a full on diagram which seems a bit ridiculous to me for 2 marks.

http://i54.tinypic.com/33m3g5w.jpg

Marker's comments:


How do I show the particle comes to rest and returns towards the origin...? + the v^2 does not become 0 part?

chuck in v=4, 16 = 16 + 6x - 2x^3

16's cancel out

0 = 3x - x^3
0 = x(3-x^2)
0 = x(root(3) - x)(root(3) +x)

so when x=root (3) velocity =0

x can't equal to -root(3)

x can = 0 --> but x=0 is at origin, means only possible way particle can turn AGAIN IS AT x=0, which obviously means that the particle must have reach the origin again after turning towards the origin at x=sqrt(3)

 

[barbernator]

chuck in v=4, 16 = 16 + 6x - 2x^3

16's cancel out

0 = 3x - x^3
0 = x(3-x^2)
0 = x(root(3) - x)(root(3) +x)

so when x=root (3) velocity =0

x can't equal to -root(3)

x can = 0 --> but x=0 is at origin, means only possible way particle can turn AGAIN IS AT x=0, which obviously means that the particle must have reach the origin again after turning towards the origin at x=sqrt(3)

I'm sorry, but there are about 10000000 things wrong with this statement

 

[weber]

>v=4
>v=0
What a magician!

 

[cssftw]

>v=4
>v=0
What a magician!

yea i'm a wizard brah. umad?