Question 1: A velocity-time graph shows a straight line from (0, 0) to (5, 20). What is the average velocity of the object during this time? Show your working.

Answer: 4 units per second

Question 2: On a velocity-time graph, the area under the curve between t=0 and t=6 seconds is 60. What does this area represent?

Answer: The total distance traveled in units

Question 3: A student claims that a flat horizontal line on a velocity-time graph indicates the object is accelerating. Is this correct? Explain your answer.

Answer: No, a flat line indicates constant velocity, meaning no acceleration.

Question 4: Plot a velocity-time graph for an object that accelerates uniformly from 0 to 10 m/s over 5 seconds.

Answer: Student draws a straight line from (0, 0) to (5, 10)

Question 5: A velocity-time graph shows a decreasing linear line from (0, 15) to (10, 0). What is the acceleration of the object?

Answer: -1.5 m/s²

Question 6: Identify the common mistake in interpreting the slope of a velocity-time graph. How can this mistake be avoided?

Answer: Mistake: Confusing the slope with the velocity; it actually represents acceleration. Avoid by reviewing the definition of slope as rise over run.

Question 7: Calculate the area under the velocity-time graph between t=0 and t=8 seconds for a graph where velocity is 0 at t=0, rises to 8 m/s at t=4, then stays constant at 8 m/s until t=8.

Answer: Area = Triangle + Rectangle = (1/2)*4*8 + 4*8 = 16 + 32 = 48 m

Question 8: A velocity-time graph shows an object with a constant velocity of 12 m/s for 10 seconds. What is the total distance traveled?

Answer: 120 meters

Question 9: Describe a common misconception students have about the area under the velocity-time graph and how to clarify it.

Answer: Misconception: Thinking the area is just length or width; it actually represents distance. Clarify by linking area to total displacement.

Question 10: A graph shows a constant negative velocity of -5 m/s over 4 seconds. What is the total displacement?

Answer: -20 meters

Question 11: A common error is to assume the slope of the velocity-time graph always indicates acceleration. When is this true and when is it false?

Answer: True when the line is linear; false when the line is curved or flat, as the slope then does not represent constant acceleration.

Question 12: Identify and correct the mistake in the following interpretation: 'A steeper slope means the object is moving faster.'

Answer: Mistake: Slope indicates acceleration, not directly the speed; a steeper slope means higher acceleration if starting from rest.