Quick questions on Kinematics: position, velocity and acceleration (TCE Mathematics Methods, Tasmania)

Sign carries direction. A positive velocity means the object moves in the positive direction; a negative velocity means it moves backwards. The object is momentarily at rest when $v=0$.

A common second style of question gives the acceleration and an initial condition and asks you to integrate. For example, if $a(t) = 6t$ with $v(0)=2$, then $v(t) = \int 6t\,dt = 3t^2 + C$, and $v(0)=2$ gives $C=2$, so $v(t) = 3t^2 + 2$. Integrating again with a starting position recovers $x(t)$.

A velocity-time graph encodes everything at a glance. The gradient of the graph at any instant is the acceleration, and the signed area between the graph and the time axis over an interval is the displacement. Area below the axis (negative velocity) counts as negative displacement, so for total distance travelled you add the magnitudes of the areas above and below separately. This graphical reading is the geometric counterpart of the calculus: gradient corresponds to differentiation, area to integration.