Question

9.what is the displacement represented by the graph in figure over the time interval from 0 s to 10.0 s?

Explanation:

Step1: Calculate the area of the triangle

The formula for the area of a triangle is \(A_{triangle}=\frac{1}{2}bh\). Here, the base \(b = 5.0\ s\) and the height \(h=10.0\ m/s\).

$$ A_{triangle}=\frac{1}{2}\times5.0\ s\times10.0\ m/s = 25\ m $$

Step2: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A_{rectangle}=lw\). Here, the length \(l = 5.0\ s\) and the width \(w = 10.0\ m/s\).

$$ A_{rectangle}=5.0\ s\times10.0\ m/s=50\ m $$

Step3: Calculate the total displacement

The total displacement is the sum of the area of the triangle and the area of the rectangle.

$$ s=A_{triangle}+A_{rectangle}=25\ m + 50\ m=75\ m $$

Answer:

\(75\ m\)