Question

match up graphs 1 - 4 with the correct description of the motion of the object for section one, and then use the section two graph to complete questions 5 - 7. graph 5 1. __ object is staying in the same place. 2. object is moving at a constant velocity 3. object is accelerating. 4. object is moving at a constant velocity and then stops/stays in the same place. 5. which section(s) of the graph show(s) an object accelerating? a) a b) b c) c d) a and c 6. which section(s) of the graph show(s) an object moving at a constant velocity? a) a b) b c) c d) a and c 7. __ which section(s) of the graph show(s) an object accelerating at a rate of about 2 m/s²? a) a b) b c) c d) a and c

Explanation:

Step1: Recall motion - graph characteristics

In a velocity - time graph, a horizontal line means constant velocity (slope = 0, so acceleration = 0), a sloped line means acceleration (non - zero slope), and a flat line at zero velocity means the object is at rest.

Step2: Match descriptions to graphs

1. An object staying in the same place has a velocity of 0. A flat line at \(v = 0\) represents this.
2. An object moving at a constant velocity has a horizontal line on a velocity - time graph (\(a=0\), \(\frac{\Delta v}{\Delta t}=0\)).
3. An object accelerating has a non - horizontal, sloped line on a velocity - time graph (\(\frac{\Delta v}{\Delta t}

eq0\)).

1. An object moving at a constant velocity and then stopping has a horizontal line followed by a flat line at \(v = 0\).

Step3: Analyze Graph 5

In Graph 5, section A is a sloped line (acceleration), section B is a horizontal line (constant velocity), and section C is a sloped line (acceleration).

Step4: Answer question 5

Accelerating sections are where the slope of the \(v - t\) graph is non - zero. In Graph 5, sections A and C have non - zero slopes. So the answer to question 5 is d) A and C.

Step5: Answer question 6

Constant velocity is represented by a horizontal line. In Graph 5, section B is horizontal. So the answer to question 6 is b) B.

Step6: Calculate acceleration for question 7

The acceleration \(a=\frac{\Delta v}{\Delta t}\). For section A, if we assume \(v_1 = 0\) at \(t_1=0\) and \(v_2 = 20\ m/s\) at \(t_2 = 20\ s\), then \(a=\frac{20 - 0}{20-0}=1\ m/s^{2}\). For section C, if we assume \(v_1 = 20\ m/s\) at \(t_1 = 50\ s\) and \(v_2=60\ m/s\) at \(t_2 = 70\ s\), then \(a=\frac{60 - 20}{70 - 50}=\frac{40}{20}=2\ m/s^{2}\). So the answer to question 7 is c) C.

Answer:

1. Graph with flat line at \(v = 0\)
2. Graph with horizontal non - zero \(v\) line
3. Graph with sloped line
4. Graph with horizontal non - zero \(v\) line followed by flat line at \(v = 0\)
5. d) A and C
6. b) B
7. c) C