/sci/ - Science & Math

[Anonymous No.4002965]

hi /sci/. Mechanics/Calculus faggot here. I fucking enjoy doing shit like this i have no idea why. Like everyone in my class hates it but when the teacher sets work i go and fucking do pages of it; not just the one question he sets. Im stumped on one question though. It states:

A particle moves in a straight line and its acceleration after t seconds is 6tms^-2. Its displacement at time t is x metres.Given that x=5 when t=1 and x=14 when t=2 find an expression for x as a fucntion of t and the value of x when t =3.

to solve this ive integrated 6t twice to get

t^3 +ct + d but now im fucking stumped. Ive tried subbing in the x#s and t and get a simultaneous equation but that doesnt seem to be helping me. any clues? thanks

[Anonymous No.4002987]

a= d²x/dt²
you found that x(t)=t^3+ct+d (I trust you)
you just replace t by 1 and 2 in that and solve the system!
x(1)=1^3+c*1+d=5
x(2)=2^3+c*2+d=14
(find c and d)

[Anonymous No.4002990]

As at t = x:

t^3 + ct + d = x

when x = 5 and t = 1

1 + c + d = 5

c + d = 4
---------------------
when x = 14 and t = 2

8 + 2c + d = 14

2c + d = 6
--------------------------
so

2c + d = 6
c + d = 4
c = 2

sub in for d.

[Anonymous No.4002993]

>>4002990
>>4002987

ahhh thanks. It seems i subbed the into c wrongly stupid error, fucks up the whole question. I got c instead of 2c?? dno how i made that mistake.I should learn to take care.

Thanks guys x