study the velocity vs. time graph shown. what is the displacement of the object from 2 seconds to 6 seconds…

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 velocity vs. time 9 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 time (s) velocity (m/s)

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 velocity vs. time 9 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 time (s) velocity (m/s)

Answer

Explanation:

Step1: Recall displacement - area relation

Displacement is area under velocity - time graph.

Step2: Identify shape of area

The area from (t = 2\ s) to (t=6\ s) is a trapezoid.

Step3: Determine trapezoid parameters

The bases of the trapezoid are (v_1 = 4\ m/s) and (v_2=8\ m/s), and height (h=(6 - 2)\ s=4\ s).

Step4: Apply trapezoid - area formula

The area formula for a trapezoid is (A=\frac{(b_1 + b_2)h}{2}), where (b_1) and (b_2) are bases and (h) is height. Substituting (b_1 = 4), (b_2 = 8) and (h = 4) gives (A=\frac{(4 + 8)\times4}{2}). [A=\frac{12\times4}{2}=24]

Answer:

24 m