displacement is the movement of an object. The units could be the distance traveled or the coordinates in space. For example. If I’m measuring the flow of labeled water in xylem sap, I might use the distance traveled from the first measurement as my measure of displacement. So the first pair of data would be (0 cm, 0 s) and the second pair might be (10.3 cm, 60 s) and a third pair is (20.1 cm, 120 s).
Velocity is the change in displacement over time. So in our example the xylem sap moved (20.1 cm - 10.3 cm) 9.8 cm during the 2nd time period, which is (120 s - 60 s) 60 s, or 9.8 cm s\(^{-1}\). Velocity is a vector quantity, meaning there is a magnitude component, which is also called speed, and a directional component. So xylem flowing up a tree at 9.8 cm s\(^{-1}\) and phloem flowing down a tree at 9.8 cm s\(^{-1}\) have different velocities but the same speed. This comparison seems absurd because all we care about is the speed in this comparison, which is the same for the xylem and phloem. But direction (and so velocity) does matter in many physiological comparisons. If you walk in a straight line at 8 miles per hour or you walk in a circle with a radius of 2 feet at 8 miles per hour than your velocity is not changing in the first but is in the second. Your inner ear senses this change in velocity and is the first step in you becoming dizzy.
Acceleration is the change in velocity over time. Your inner ear contains an organ that functions as an accelerometer. We cannot sense velocity - inside a plane I cannot tell if the plane is sitting on the tarmac or flying at 500 mph - but we can sense change in velocity (or acceleration). Acceleration also is a vector quantity. Importantly, in everyday language we use “accelerate” to mean “getting faster” and “decelerate” to mean “slowing down”, but in science “getting faster” is positive acceleration and “slowing down” is negative acceleration (that is, a negative number), and this is with respect to some direction.
Jerk is the change in acceleration over time. We won’t talk about jerk!