Question

study the velocity vs. time graph shown. what is the displacement of the object from 2 seconds to 6 seconds? 4 m 8 m 16 m 24 m

Explanation:

Step1: Recall displacement - area relation

Displacement is area under v - t graph.

Step2: Calculate area of trapezoid

The area of a trapezoid is $A=\frac{(a + b)h}{2}$, where $a$ and $b$ are the lengths of the parallel sides and $h$ is the height. At $t = 2s$, $v=4m/s$ and at $t = 6s$, $v = 8m/s$, and $h=6 - 2=4s$. So $a = 4m/s$, $b = 8m/s$, $h = 4s$. Then $A=\frac{(4 + 8)\times4}{2}$.

Step3: Compute the area

$A=\frac{12\times4}{2}=24m$.

Answer:

$24m$