Question

question 5 (3 points) (02.04 mc) an object starts at rest. its acceleration over 30 seconds is shown in the graph below. acceleration vs. time use the graph above to determine the change in speed of the object between 20 and 30 seconds? a 6 m/s b 30 m/s c 60 m/s d 180 m/s

Explanation:

Step1: Recall acceleration - speed relation

The change in speed $\Delta v$ is given by the area under the acceleration - time graph. For the time interval from $t = 20\ s$ to $t=30\ s$, the acceleration - time graph is a right - angled triangle.

Step2: Identify base and height of triangle

The base of the triangle $\Delta t=30 - 20=10\ s$. From the graph, assume the maximum acceleration in this interval is $a = 6\ m/s^{2}$.

Step3: Calculate area of triangle

The area of a triangle is $A=\frac{1}{2}\times base\times height$. Here, $A=\frac{1}{2}\times(30 - 20)\times6$.
\[A=\frac{1}{2}\times10\times6 = 30\ m/s\]

Answer:

B. 30 m/s