Understanding derivatives is important when we look at how things move. They help us see some key ideas:

1. Tangent Lines: A derivative at a certain point shows us the slope of the tangent line. This slope tells us how fast something is changing at that exact moment.

2. Velocity: The first derivative of position, written as $s'(t)$, tells us the velocity. For example, if the position is $s(t) = t^2$, then the velocity is $s'(t) = 2t$.

3. Acceleration: The second derivative, $s''(t)$, helps us find acceleration. Using our earlier example, $s''(t) = 2$ shows that there is a constant acceleration.

By understanding these ideas, we can better read motion graphs. This helps us make predictions about how things will move in the future and find important points on the graph.