Question

question 5 (4 points)
(02 04 mc)
an acceleration versus time graph is shown.
calculate the change in velocity from 20 to 25 seconds.
a 3 m/s
b 7.5 m/s
c 15 m/s
d 75 m/s

Explanation:

Step1: Recall the relationship between acceleration - time graph and velocity

The change in velocity $\Delta v$ over a time - interval is given by the area under the acceleration - time ($a - t$) graph for that time - interval.

Step2: Calculate the area of the trapezoid for the time interval 20 - 25 s

The acceleration - time graph from $t = 20\ s$ to $t = 25\ s$ forms a trapezoid. The formula for the area of a trapezoid is $A=\frac{(b_1 + b_2)h}{2}$, where $b_1$ and $b_2$ are the lengths of the parallel sides and $h$ is the height.
From the graph, at $t = 20\ s$, $a_1=0\ m/s^2$, at $t = 25\ s$, $a_2 = 3\ m/s^2$, and the time interval $\Delta t=h = 5\ s$.
Using the area formula for the trapezoid of the $a - t$ graph:
\[

$$\begin{align*} \Delta v&=\frac{(0 + 3)\times5}{2}\\ &=7.5\ m/s \end{align*}$$

\]

Answer:

B. 7.5 m/s