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 0≤t≤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.

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.