Expert: Ahmed Salami - 2/13/2009

Question
QUESTION: A particle moves along the X-axis so that at time t its position is given by x(t)=sin(pi*t^2) for -1 ≤ t ≤ 1
a.) find the velocity at time t
b.) find the acceleration at time t
c.) for what value of t does the particle change direction?
d.) Find all values of t for which the particle is moving to the left

ANSWER: Hi Linrosa,
a)x = sin(#t^2)
 v = dx/dt
   = 2#t.cos(#t^2)

b)a = dv/dt
   = [2#t.2#t.-sin(#t^2)  +  2#.cos(#t^2)]  
   = -4#^2.t^2.sin(#t^2)  +  2#.cos(#t^2)

c)It changes direction when v = 0,
2#t.cos(#t^2) = 0
i.e when 2#t = 0 or cos(#t^2) = 0
t = 0 or #t^2 = #/2 i.e t = (sqrt2)/2

d)We need to find all values of t for which x < 0 i.e
sin(#t^2) < 0
# < #t^2 < 2#
1 < t^2 < 2
clearly, these values dont go with the original constraint -1 ≤ t ≤ 1 and so i'm forced to say x is never < 0

You know, you can always get back to me.

Regards


You know, instead of making the stupid ratings you could have told me you didnt understand the fundamentals of calculus that even people with half a brain understand.

---------- FOLLOW-UP ----------

QUESTION: First of off don't be immature and rude. This is suppose to be a friendly site. I do understand the fundamentals of calculus it was just that first off your answers contains # and are confusing. Second off they are wrong. If you don't agree, you can ask the other 4 experts I asked the same question to who all got the same answer that you couldn't. Also my AP Calculus teacher and my entire AP Calculus confirmed my answer was right. Therefore do not be rude since you got something wrong. You can always try to improve yourself. All I wanted was to double check my answers.

Answer
Yes, its a friendly site but some people decide to give you unfriendly ratings because of a mix up which i clearly assumed and stated at the end of the solution. I remember asking you to get back to me in case you find the mix up. I'm not too proud to correct a mistake but deciding to dish out unfair ratings, something i've been working on for years, is plain heartbreaking. There have been people who've noticed simple human errors in the past and have gotten back to me and in the end we all make a laugh out of it. I've been here more than five years and all i have to show are my ratings which i'm ever proud of. This is elementary kinematics and you think i should improve myself on it!!! Its so easy to figure out i used # to represent pi, if you checked. Anyway, you could be nice enough to show me, apart from the last question mix up(x instead of v), where its all supposedly wrong.
Thank you.