Question:

The graph below represents the position versus time for an object in motion. Use the graph to answer the following questions.

a) Describe the motion of the object during each of the following time intervals:

i) 0 to 4 seconds ii) 4 to 8 seconds iii) 8 to 12 seconds

b) Calculate the average velocity of the object during the entire motion.

c) Determine the acceleration of the object during each of the time intervals mentioned in part a).

Answer:

a)

i) During the time interval 0 to 4 seconds, the object is moving in the positive direction with a constant velocity. This is evident from the straight line with a positive slope on the graph. The object is moving away from the origin at a constant speed.

ii) During the time interval 4 to 8 seconds, the object is at rest. The position remains constant at 12 meters, resulting in a horizontal line on the graph. The object has zero velocity during this interval.

iii) During the time interval 8 to 12 seconds, the object is moving in the negative direction. The position decreases with time, indicating motion towards the origin. The object is moving with a constant velocity in the negative direction.

b) The average velocity of an object is determined by dividing the change in position by the change in time. In this case, the position changes from 0 meters to -12 meters over a time interval of 12 seconds.

Average velocity = (Change in position) / (Change in time) Average velocity = (-12 meters - 0 meters) / (12 seconds - 0 seconds) Average velocity = -12 meters / 12 seconds Average velocity = -1 meter/second

Therefore, the average velocity of the object during the entire motion is -1 meter/second.

c) Acceleration can be calculated from the slope of the position versus time graph. The slope represents the rate of change of velocity.

i) Since the object moves with constant velocity during the interval 0 to 4 seconds, the acceleration is zero. The slope of the graph is constant.

ii) As the position remains constant during the interval 4 to 8 seconds, the object has zero velocity and zero acceleration.

iii) During the interval 8 to 12 seconds, the object moves with a constant velocity in the negative direction. The slope of the graph is constant, indicating zero acceleration.

In summary:

• Acceleration during the interval 0 to 4 seconds: 0 m/s²
• Acceleration during the interval 4 to 8 seconds: 0 m/s²
• Acceleration during the interval 8 to 12 seconds: 0 m/s²