Question

the graph below represents the motion of an object.

1. how long does it take for the object to move 30 meters? 2. how far does the object travel in 2 seconds?
2. the object is in (circle one: dynamic / static) equilibrium because it moves ______________ meters every second.

Explanation:

Step1: Determine the relationship from the graph

The graph is a position - time graph. The position \(y\) and time \(x\) follow a linear relationship \(y = mx + b\), where \(b = 0\) (passes through the origin) and the slope \(m\) is the velocity. From the graph, when \(x = 1\) s, \(y=10\) m, so the velocity \(v=\frac{\Delta y}{\Delta x}= 10\) m/s.

Step2: Solve for the time to move 30 meters

We know that \(v=\frac{d}{t}\), so \(t=\frac{d}{v}\). Given \(d = 30\) m and \(v = 10\) m/s, then \(t=\frac{30}{10}=3\) s.

Step3: Solve for the distance in 2 seconds

Using \(d=v\times t\), with \(v = 10\) m/s and \(t = 2\) s, we get \(d=10\times2 = 20\) m.

Step4: Determine the equilibrium state

The object is moving at a constant velocity. An object in motion with a constant velocity is in dynamic equilibrium. The velocity is 10 m/s, so it moves 10 meters every second.

Answer:

1. 3 s
2. 20 m
3. DYNAMIC; 10