Question

question 3 (3 points)
(02.04 mc)
a speed - time graph is shown below.
speed vs. time
how far did the object travel by the end of eight seconds, according to the graph above?
a it traveled 12 centimeters.
b it traveled 16 centimeters.
c it traveled 24 centimeters.
d it traveled 32 centimeters.

Explanation:

Step1: Identify the shape under the speed - time graph

The area under a speed - time graph gives the distance traveled. The graph has a triangle from \(t = 0\) to \(t=4\) seconds and a rectangle from \(t = 4\) to \(t = 8\) seconds.

Step2: Calculate the area of the triangle

The formula for the area of a triangle is \(A_{triangle}=\frac{1}{2}\times base\times height\). The base of the triangle is \(4\) s and the height is \(4\) cm/s. So \(A_{triangle}=\frac{1}{2}\times4\times4 = 8\) cm.

Step3: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A_{rectangle}=length\times width\). The length of the rectangle is \(4\) s and the width is \(4\) cm/s. So \(A_{rectangle}=4\times4 = 16\) cm.

Step4: Calculate the total distance

The total distance \(d\) is the sum of the area of the triangle and the area of the rectangle. \(d=A_{triangle}+A_{rectangle}=8 + 16=24\) cm.

Answer:

C. It traveled 24 centimeters.