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havj0y · Dec 11, 2011, 05:35 PM

a particle is moving along a straight line so that after t seconds after passing through a fixed point O on the line, its velocity is given by v(t)=t*sin(Ï€/3*t)
a) find the values of t for which v(t)=0 given that 0â‰¤tâ‰¤6

b) write down a mathematical expression for the total distance traveled by the particle in the particle in the first six seconds after passing through O. And find this distance.

Aurora2000 · Dec 12, 2011, 09:15 AM

The display is not readable, it is not possible to directly copy math formulas.

I will answer the general case, where the speed is $v(t):=t\sin (X(t))$ , with
$X(t)$ a function of t.

a) $v(t)=0$ is verified by putting $t=0$ or $X(t)=n\pi$ ,
where $n$ can be an arbitrary integer.

b) To get the distance $s(t)$ from speed [/math]v(t)[/math], remember that

$v=\frac{ds}{dt}$ , thus
$s(T)= \int_0^T v(t)dt +C$
where C is a constant determined by initial conditions.

If you want more details you should post a correct display of math formulas, using the "math"
environment.