In one dimension, motion can be described by a coordinate $x(t)$. Displacement is $\Delta x = x_f - x_i$. Positive and negative signs indicate direction relative to the chosen axis.

Average velocity is $v_{\text{avg}} = \Delta x/\Delta t$. Instantaneous velocity is $v = dx/dt$. Acceleration is $a = dv/dt = d^2x/dt^2$. The sign of acceleration tells you how velocity changes, not necessarily whether the object speeds up or slows down.

When acceleration is constant, the motion equations are $v = v_0 + at$, $x = x_0 + v_0 t + \tfrac{1}{2}at^2$, and $v^2 = v_0^2 + 2a(x-x_0)$. These are powerful because they connect kinematics without needing time in every problem.

The slope of an $x$-$t$ graph gives velocity. The slope of a $v$-$t$ graph gives acceleration. The area under a $v$-$t$ graph gives displacement, and the area under an $a$-$t$ graph gives change in velocity.