what is the total displacement over the time interval of 0-7 seconds?

Explanation:

Step1: Identify the method

The displacement is the area under the velocity - time graph.

Step2: Divide the graph into shapes

The graph can be divided into a rectangle from (t = 0) to (t = 5) and a trapezoid from (t=5) to (t = 7).

Step3: Calculate the area of the rectangle

The rectangle has a height (v = 6\ m/s) and base (b = 5\ s). The area of the rectangle (A_1=v\times t=6\times5 = 30\ m).

Step4: Calculate the area of the trapezoid

The trapezoid has bases (b_1 = 6\ m/s) and (b_2=4\ m/s) and height (h = 2\ s). The area of a trapezoid is (A=\frac{(b_1 + b_2)h}{2}), so (A_2=\frac{(6 + 4)\times2}{2}=10\ m).

Step5: Calculate the total displacement

The total displacement (d=A_1+A_2=30 + 10=40\ m).

Answer:

(40\ m)