Question

(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 of the graph.

Step2: Analyze first part of graph

The initial slope of the graph is $\frac{\Delta x}{\Delta t}$. For the first part of the motion, if we consider the first 4 - second interval, assume the position changes from 0 to 4 cm in 4 seconds. The velocity $v_1=\frac{4 - 0}{4-0}=1$ cm/s.

Step3: Analyze middle part of graph

The middle part of the graph (from 4 - 8 seconds) has a slope of 0. A slope of 0 on a position - time graph means the object is at rest.

Step4: Analyze last part of graph

For the last part of the motion (from 8 - 10 seconds), assume the position changes from 4 cm to 8 cm in 2 seconds. The velocity $v_2=\frac{8 - 4}{10 - 8}=2$ cm/s.

Answer:

b. The object moves forward at 1 cm/s, stops, and then increases velocity to 2 cm/s