Question

An eagle is flying around and its velocity vvvv as a function of time tttt is given in the graph below where rightwards is the positive velocity direction.

A set of black coordinate axes are given with the vertical axis labeled "v (m/s)" and the horizontal axes labeled "t (s)". A curve that relates v to t is shown in blue. It begins with a straight line of endpoints (0,-2) and (3,4). This first line is connected to a second line with endpoints (3,4) and (4,4).
A set of black coordinate axes are given with the vertical axis labeled "v (m/s)" and the horizontal axes labeled "t (s)". A curve that relates v to t is shown in blue. It begins with a straight line of endpoints (0,-2) and (3,4). This first line is connected to a second line with endpoints (3,4) and (4,4).
What is the eagle's displacement Δx\Delta xΔxdelta, x from t=1.0 st=1.0\,\text st=1.0st, equals, 1, point, 0, start text, s, end text to 4.0 s4.0\,\text s4.0s4, point, 0, start text, s, end text?

Answer 1

9514 1404 393

Answer:

8 units

Explanation:

Displacement is the area under the velocity curve. The area of interest is in the shape of a trapezoid, so we can use the formula ...

A = (1/2)(b1 +b2)h

to find the area.

Here, b1=3, b2=1, h=4, so the area is ...

A = (1/2)(3 +1)(4) = 8

The displacement is 8 units in the time from t=1 to t=4.