position

Position tells you where an object is relative to a chosen origin. In mechanics it is usually written as a vector, e.g.

$$\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}$$

The important habit: position is not just “where the object is”; it is where it is in a coordinate system you chose. Change the origin and the position values change, even though the physical situation did not.

Position vs displacement

• Position: location relative to an origin, $\vec{r}(t)$.
• Displacement: change in position, $\Delta \vec{r}={\vec{r}}_f-{\vec{r}}_i$.

Distance is the total path length travelled, while displacement only cares about start and end. Walk 3 m east then 3 m west: distance is 6 m, displacement is 0.

Links

Velocity is the rate of change of position. Kinematic problems normally start by writing down initial position, final position/displacement, velocity, acceleration, and time.

Units: Metre.

Coordinate habit

Pick axes to make the problem simple. For motion on a ramp, one axis along the ramp is usually cleaner than horizontal/vertical axes. Once chosen, keep the convention fixed: signs in Velocity, acceleration, and displacement only make sense relative to that coordinate choice.