# calculus help

A particle is moving with the given data. Find the position of the particle.

a(t)= (t^2 - 5t +7) , s(0)=0 , s(1)=20

Thanks!

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1. a = t^2-5t+7
v = 1/3 t^3 - 5/2 t^2 + 7t + C1
s = 1/12 t^4 - 5/6 t^3 + 7/2 t^2 + C1*t + C2
plugging s(0) and s(1), we have

C1 = 0
1/12 - 5/6 + 7/2 + 0 + C2 = 20
C2 = 69/4
so,
s(t) = 1/12 t^4 - 5/6 t^3 + 7/2 t^2 + 69/4

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2. When I put your answer into WebAssign it marked as wrong so are you sure this is the right answer?

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3. well, pretty sure. Do you see any errors in my work?

wolframalpha agrees with me.

http://www.wolframalpha.com/input/?i=solve+y%22+%3D+x^2-5x%2B7+where+y%280%29%3D0+and+y%281%29%3D20

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4. actually, I do see a mistake.

C2 = 0
C1 = 69/4

s(t) = 1/12 t^4 - 5/6 t^3 + 7/2 t^2 + 69/4 t

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