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## #1 2006-04-11 20:50:27

stardust
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### A mechanics question

I was doing my maths hw when i got stuck on this M1 exam paper question.

3. In a simple model for the motion of a car, its velocity,v, at time t seconds is given by
v=(3t² - 2t + 8)i + (5t +6)j ms-¹

a) Calculate the speed of the car when t=0.

b) Find the values of t for which the velocity of the car is parallel to the vector (i+j).

c) Why would this model not be appropriate for large values of t?

I have done a) and made it 10ms-¹ which agrees with the answers i have been supplied. I am confused on how to do b) and any help would be appreaciated.
Thanks

## #2 2006-04-11 23:21:45

George,Y
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### Re: A mechanics question

if a vector ai+bj is parallel to the vector i+j, it means ai+bj=k(i+j)
since i and j are not parallel to each other, the only solution is a=k, b=k
Hence a=b
3t² - 2t + 8=5t +6
3t²-7t+2=0
(3t-1)(t-2)=0
t=1/3 or t=2

for c, the speed cannot grow up forever.

X'(y-Xβ)=0

stardust
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Thanks

## #4 2006-04-12 09:08:58

MathsIsFun

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### Re: A mechanics question

Oh, and "c" is because of "c"

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

George,Y
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:p

X'(y-Xβ)=0