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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: thisongaintgottaname on October 27, 2009, 01:56:11 pm

Title: velocity
Post by: thisongaintgottaname on October 27, 2009, 01:56:11 pm: heyy!

i have a question here,

A particle moves in a straight line with acceleration of a=x+6 at time t. Given that x=1,v=7, the velocity of the particle is?

is it 土(x+6) or is it just -(x+6) ?

thank you very much!
Title: Re: velocity
Post by: NE2000 on October 27, 2009, 02:04:12 pm: $a= x + 6$
$d/dx(0.5v^{2}) = x + 6$
$\frac{v^2}{2} = \frac{x^2}{2} + 6x + c$

Sub in x = 1, v = 7

$\frac{49}{2} = \frac{1}{2} + 6 + c$

$c = 18$

$\frac{v^2}{2} = \frac{x^2}{2} + 6x + 18$

$v^2 = x^2 + 12x + 36$
$v = \pm \sqrt{x^2 + 12x + 36}$
$v = \pm (x+6)$
lol sorry for all that working, I just read your question properly (so drained straight after exam right now :P)

but when x = 1, v = 7

Hence take positive as if you took negative then v = -7

so yeah
$v = x + 6$
Title: Re: velocity
Post by: thisongaintgottaname on October 27, 2009, 02:17:55 pm: woo long working! thank you NE2000!!xD

this is a MAV 2004 exam question. i doubted the accuracy of the answer as it states the answer be 土(x+6). i am sure the solution is wrong now.

thanks again!! :D
Title: Re: velocity
Post by: Hooligan on October 27, 2009, 02:19:52 pm: Quote from: thisongaintgottaname on October 27, 2009, 01:56:11 pm
heyy!

i have a question here,

A particle moves in a straight line with acceleration of a=x+6 at time t. Given that x=1,v=7, the velocity of the particle is?

is it 土(x+6) or is it just -(x+6) ?

thank you very much!

the first time I read your question... the answer of 7 came to head immediately, but then after reading the question again, I realised it was asking for the velocity function in terms of t. haha. lol :D
Title: Re: velocity
Post by: NE2000 on October 27, 2009, 03:26:55 pm: ^^ lol. Normally it should say the velocity at time 't'. I wonder whether you'd get a mark for saying 7... (wouldn't bet on it)