Multi-step Displacement

When an object undergoes multiple movements in sequence, we find its total displacement by adding the individual displacements together.

For horizontal motion with displacements $\Delta x_1$, $\Delta x_2$, $\Delta x_3$, etc., the total displacement is:

Positive values represent rightward movement and negative values represent leftward movement. For example, if an object moves right by $\Delta x_1 = 5 \text{ m}$ , left by $\Delta x_2 = -3 \text{ m}$ , then right by $\Delta x_3 = 2 \text{ m}$ :

The total displacement is:

For vertical motion with displacements $\Delta y_1$, $\Delta y_2$, $\Delta y_3$, etc.:

Positive values represent upward movement and negative values represent downward movement. If an object moves up by $\Delta y_1 = 8 \text{ m}$ , down by $\Delta y_2 = -5 \text{ m}$ , down by $\Delta y_3 = -2 \text{ m}$ , then up by $\Delta y_4 = 3 \text{ m}$ :