Final answer:
Resultant displacement is the vector sum of all displacements, calculated by summing vector components or graphically using the head-to-tail method. It has both magnitude and direction, crucial for understanding the change in position of a moving object.
Step-by-step explanation:
The resultant displacement is defined as the vector sum of all individual displacement vectors that a moving object experiences. In physics, displacement is a vector quantity, meaning it has both magnitude and direction. For multiple displacements, as in the problem with vectors D₁, D₂, D₃, D₄, and D₅, the resultant displacement is found by vector addition. The calculation provided shows the individual components being summed up algebraically, considering their directions, to give a final resultant displacement of -32 cmû.
In graphic terms, displacement vectors can be represented using scaled arrows on a graph, oriented correctly as per their direction. The head-to-tail method allows for a visual representation of vector addition to determine the resultant displacement. For example, the resultant displacement R can be found graphically using a scale and a protractor by combining multiple vectors like A, B, and C, considering their magnitudes and direction angles with the horizontal.
When calculating displacement using a velocity-time graph, the area under the graph represents the total displacement. The overall displacement can be represented as the sum of the areas of shapes like rectangles and triangles under the velocity-time curve, which represent the motion of the object over time.