Question

Study the velocity vs. time graph shown.

What is the displacement of the object from 2 seconds to 6 seconds?
4 m
8 m
16 m
24 m

Answer 1

24

edge22

Explanation:

area of triangle = 8

area of rectangle = 16

16+8=24

Answer 2

8 m.

Explanation:

The instantaneous displacement is

`ds=v*dt`

and to find
`s` from
`t_1` to
`t_2` we integrate

`s=\int_(t_1)^(t_2) v*dt`

since this integral is the area is the under the graph, the displacement
`s` 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:

`A = (1)/(2)(\Delta v ) (\Delta t)= (1)/(2) (8-4)(6-2)\\\\\boxed{A=8}`

The area under the graph is 8, that means the displacement from 2 seconds to 6 seconds is 8 meters.