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Calculus/Velocity/time/distance

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Expert: Vineeth Venugopal - 1/23/2009


Question
A particle moves along a straight line such that its velocity, v, at position, x, is
given by v=x^6. Find the time it takes for the particle to move from x=5 to
x=10.

Answer
hi Katarina,

the relation between velocity, distance and time is given by dx/dt=v;

rewriting, we have that dt=dx/v. integrating both sides, T= integral(a to b) dx/v;
T = integral (5-10)(dx/v)= integral(5-10) (dx/x^6)= integral(5-10) (x^-6dx)= [-6x^(-5)]=-6[10^(-6)-5^(-6)]=6[10^(-6)-5^(-6)].

 Thus, this is the answer. I am sorry if this is a bit shaky on the notations but there is no provision for the integration sign here. ask me if this is not clear to you.

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Vineeth Venugopal

Expertise

I can answer most questions that relate to engineering mathematics like Laplacian transforms, advanced calculus, Integral transforms, tensors, Multiple integrals, trigonometry, sequences and probability. I have a special fondness for Number theory particularly prime numbers and their properties. I keep myself updated and sharp. Also, I have read extensively on the history of mathematics and the philosophy behind it. I am open to the various view points on the topic.

Experience

I am an engineer myself and have worked extensively in the field. I love maths and it is something that i think cames naturally to me.

Education/Credentials
Undergraduate degree in Ceramic Engineering, Masters in Mathematics, PhD in finite Analysis

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