particle moves in line acc. to s(t) = t^4 - 6t^3 + 12t^2 - 10t + 3, t in secs.

[Nalaka]

A particle moves in a line according to the distance formula:

. . . . .\(\displaystyle s(t)\, =\, t^4\, -\, 6t^3\, +\, 12t^2\, -\, 10t\, +\, 3\)

where t is time in seconds. At what time does the direction of the motion change?

 

[Deleted member 4993]

For that first you need to get the "speed function" by differentiating the given "displacement function".

What are your thoughts?

Please share your work with us ...even if you know it is wrong

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...Before-Posting

 

[Nalaka]

Hi Denis,
Thanks for your reply. I really appreciate that. It helped me to understand the question and helped to take a good start. Please see my workings below. So according to that I assume it change the direction when t=2. Please clarify.

 

[stapel]

A particle moves in a line according to the distance formula:

. . . . .\(\displaystyle s(t)\, =\, t^4\, -\, 6t^3\, +\, 12t^2\, -\, 10t\, +\, 3\)

where t is time in seconds. At what time does the direction of the motion change?

From your reply to the second helper's hint, I will guess that you posted this to "Geometry and Trig" because you haven't yet taken calculus. (That's why you didn't understand the first helper's hint, to use the standard method of differentiation.)

What method has your class gone over for finding the x-values (or, in this case, the t-values) at which a function changes direction? Are you supposed to be finding local max/min points in your graphing calculator, using numerical methods, or what? A scan of a worked example, similar to this one, could be helpful for our understanding what your class is probably expecting of you.

Thank you!