Question

question 2 (3 points)
(02.04 mc)
a position time graph is shown below.
position vs. time
which statement accurately describes the motion of the object in the graph above over 10 seconds?
a the object moves forward at 1 cm/s, stops, and then continues at the same velocity.
b the object moves forward at 1 cm/s, stops, and then increases velocity to 2 cm/s.
c the object is at rest for 4 seconds and then moves forward for 4 seconds at 1 cm/s.
d the object is at rest for 3 seconds and then decreases velocity to 1 cm/s for 3 seconds.

Explanation:

Step1: Recall velocity - position - time relation

Velocity on a position - time graph is slope. A flat line means zero velocity (object at rest), and a non - zero slope means non - zero velocity.

Step2: Analyze first part of motion

From \(t = 0\) to \(t=4\) s, the slope of the position - time graph is \(\frac{\Delta x}{\Delta t}=\frac{4 - 0}{4-0}=1\) cm/s. The object moves forward at 1 cm/s.

Step3: Analyze middle part of motion

From \(t = 4\) s to \(t = 6\) s, the position does not change (\(\Delta x=0\)). The slope is 0, so the object is at rest.

Step4: Analyze last part of motion

From \(t = 6\) s to \(t = 10\) s, the slope is \(\frac{\Delta x}{\Delta t}=\frac{8 - 4}{10 - 6}=1\) cm/s. The object continues at the same 1 cm/s velocity.

Answer:

A. The object moves forward at 1 cm/s, stops, and then continues at the same velocity.