2. what is the displacement represented by the graph over 0 to 6 seconds?\na. 9 m n\nb. 27 m s\nc. 0 m\nd…
2. what is the displacement represented by the graph over 0 to 6 seconds?\na. 9 m n\nb. 27 m s\nc. 0 m\nd. 27 m n\ne. 9 m s
Answer
Explanation:
Step1: Recall displacement - area under v - t graph
Displacement is given by the area under the velocity - time graph.
Step2: Divide the graph into shapes
The graph from (t = 0) to (t=6\ s) can be divided into a rectangle from (t = 0) to (t = 3\ s) and a triangle from (t=3\ s) to (t = 6\ s).
Step3: Calculate area of rectangle
For the rectangle, (v=6\ m/s) and (t = 3\ s). Area of rectangle (A_{1}=v\times t=6\times3 = 18\ m).
Step4: Calculate area of triangle
For the triangle, base (b=6 - 3=3\ s) and height (h = 6\ m). Area of triangle (A_{2}=\frac{1}{2}\times b\times h=\frac{1}{2}\times3\times6 = 9\ m).
Step5: Calculate total displacement
Total displacement (A=A_{1}+A_{2}=18 + 9=27\ m). The velocity is positive throughout, so the direction is the positive direction.
Answer:
d. (27\ m\ [N])