\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} A charged particle moves along the
$x$-axis under the influence of an electric field. The field strength
varies with time, and as a result the velocity of the particle is
complicated. The position of the particle at time $t$ is written as
$x= x(t)$ and the velocity of the particle at time $t$ is written as
$v=v(t)$.

\noindent Suppose we know that $x(0)=0$, and also that
$$v(t) = \cases{ 2t-1, &if $ 0 \le t \le 1$\cr
                 4t-3, &if $ 1 \le t \le 2$\cr
                 6t-7, &if $2 \le t \le 3$\cr}\, .$$

\noindent What is $x(1)$? What is $x(2)$? What is $x(3)$? Sketch the
graphs of $x=x(t)$ and $v=v(t)$.

\vfil\eject\end