Question

1. what is the displacement represented by the graph over 0 to 6 seconds?

a. 9 m n
b. 27 m s
c. 0 m
d. 27 m n
e. 9 m s

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. \(27\ m\ [N]\)