Question

a v-t graph is a triangle from 0 to 12 m/s over 6 s. displacement: 72 m, 6 m, 36 m, 12 m

Explanation:

Step1: Recall displacement from v-t graph

The displacement from a velocity - time (v - t) graph is given by the area under the v - t curve. For a triangular v - t graph, the area of a triangle is given by the formula \(A=\frac{1}{2}\times base\times height\).
Here, the base of the triangle (time interval) \(t = 6\ s\) and the height of the triangle (maximum velocity) \(v=12\ m/s\).

Step2: Calculate the area (displacement)

Using the formula for the area of a triangle, we substitute the values of base and height.
\(Displacement=\frac{1}{2}\times t\times v\)
Substitute \(t = 6\ s\) and \(v = 12\ m/s\) into the formula:
\(Displacement=\frac{1}{2}\times6\ s\times12\ m/s\)
First, calculate \(\frac{1}{2}\times6 = 3\). Then, \(3\times12=36\ m\).

Answer:

36 m (corresponding to the option with 36 m)