Question

1. describe the motion of the object in words. 2. calculate the velocity of the object for each time the object changes its speed. (position vs. time graph: x - axis time (seconds) 0–8, y - axis position (meters) 0–4. graph line: from (0,0) to (2,4), horizontal to (3,4), then to (7,0), (8,0))

Explanation:

Sub - question 1: Describe the motion of the object in words.

• From \(t = 0\) to \(t = 2\) seconds: The object's position increases from 0 to 4 meters. Since position - time graph slope represents velocity, a positive slope here means the object is moving with a constant positive velocity (speeding up? No, constant velocity as slope is constant) in the positive direction.
• From \(t = 2\) to \(t = 3\) seconds: The position of the object remains at 4 meters. A zero slope on a position - time graph means the object has zero velocity, so it is at rest.
• From \(t = 3\) to \(t = 7\) seconds: The object's position decreases from 4 meters to 0 meters. A negative slope on the position - time graph means the object is moving with a constant negative velocity (moving in the negative direction) back towards the starting point.

Velocity \(v=\frac{\Delta x}{\Delta t}\), where \(\Delta x\) is the change in position and \(\Delta t\) is the change in time.

Step 1: Velocity from \(t = 0\) to \(t = 2\) s

\(\Delta x=4 - 0=4\) m, \(\Delta t = 2-0 = 2\) s.
\(v_1=\frac{\Delta x}{\Delta t}=\frac{4}{2}=2\) m/s.

Step 2: Velocity from \(t = 2\) to \(t = 3\) s

\(\Delta x = 4 - 4=0\) m, \(\Delta t=3 - 2 = 1\) s.
\(v_2=\frac{\Delta x}{\Delta t}=\frac{0}{1}=0\) m/s.

Step 3: Velocity from \(t = 3\) to \(t = 7\) s

\(\Delta x=0 - 4=- 4\) m, \(\Delta t = 7 - 3=4\) s.
\(v_3=\frac{\Delta x}{\Delta t}=\frac{-4}{4}=- 1\) m/s.

Answer:

From \(t = 0\) to \(t = 2\) s, the object moves with constant positive velocity (towards positive direction) from position 0 m to 4 m. From \(t = 2\) to \(t = 3\) s, the object is at rest (position remains 4 m). From \(t = 3\) to \(t = 7\) s, the object moves with constant negative velocity (towards negative direction) from 4 m back to 0 m.

Sub - question 2: Calculate the velocity of the object for each time the object changes its speed.