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Calculus/Antiderivative?

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Expert: Alon Mandes - 11/17/2008


Question
A particle is moving with the given data. Find the position of the particle.
a(t) = t2 - 4t + 8
s(0) = 0
s(1) = 12

Find s(t).

Answer
The acceleration is a(t)=t^2-4t+8, to find the position equation we must integrate twice : ("1st integration gives us the velocity").
So,
V(t)=∫a(t) dt = ∫t^2-4t+8 dt = (1/3)t^3-2t^2+8t+C
S(t)=∫V(t) dt = ∫(1/3)t^3-2t^2+8t+C dt=
(1/12)t^4-(2/3)t^3+4t^2+Ct+D.
Now we will find C & D from the initial conditions :
S(0)=0 -> D=0
S(1)=12 -> (1/12)-(2/3)+4+C=12 -> c=8.58

Alon.  

Calculus

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Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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