Answer:
8 m.
Step-by-step explanation:
The instantaneous displacement is
[tex]ds=v*dt[/tex]
and to find [tex]s[/tex] from [tex]t_1[/tex] to [tex]t_2[/tex] we integrate
[tex]s=\int_{t_1}^{t_2} v*dt[/tex]
since this integral is the area is the under the graph, the displacement [tex]s[/tex] is the area under the graph of velocity vs. time graph.
Now having said that, let us calculate the area of the graph from 2 seconds to 6 seconds:
[tex]A = \frac{1}{2}(\Delta v ) (\Delta t)= \frac{1}{2} (8-4)(6-2)\\\\\boxed{A=8}[/tex]
The area under the graph is 8, that means the displacement from 2 seconds to 6 seconds is 8 meters.
