What is the position of a particle at time #t=2# if a particle moves along the x axis so that at any time #t>0#, the velocity is given by #v(t)=4-6t^2#, and at position #x=7# at #t=1#?

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Answer 1 · 2015-02-05T14:40:09

The answer is: #x=-3#.

The law that gives the position of the particle at the time #t# is given by the integral:

#x(t)=int(4-6t^2)dt=4t-6t^3/3+c=4t-2t^3+c#.

To find #c#, we can use the intial conditions:

#x(1)=7#,

so:

#7=4-2+crArrc=5#.

So the law becomes:

#x(t)=4t-2t^3+5#.

Now we can use it to find the positition at the time #t=2#:

#x(2)=8-16+5=-3#.