Question

draw particle - model diagrams with vectors to represent the indicated motion.
a person speeding up
a person slowing down
get it? analyze what do increasing and decreasing lengths of velocity vectors indicate on a motion diagram?
identify two main ideas about the direction of acceleration.
two main ideas about the direction of acceleration is
get it? describe the motion of an object if its velocity and acceleration vectors have opposite signs

Explanation:

Step1: Drawing for person speeding up

Draw a series of dots representing the person's position at equal - time intervals. The velocity vectors are drawn as arrows starting from each dot. For a person speeding up, the length of the velocity vectors increases with time and they all point in the same direction, indicating the direction of motion.

Step2: Drawing for person slowing down

Draw a series of dots for the person's position at equal - time intervals. The velocity vectors are arrows starting from each dot. For a person slowing down, the length of the velocity vectors decreases with time and they all point in the direction of the initial motion.

Step3: Analyzing velocity vector lengths

Increasing lengths of velocity vectors on a motion diagram indicate that the object is speeding up (accelerating in the direction of motion). Decreasing lengths of velocity vectors indicate that the object is slowing down (decelerating or accelerating in the opposite direction of motion).

Step4: Identifying acceleration direction ideas

1. When the acceleration and velocity are in the same direction, the object speeds up. 2. When the acceleration and velocity are in opposite directions, the object slows down.

Step5: Describing motion with opposite - signed vectors

If the velocity and acceleration vectors have opposite signs, the object is slowing down. The acceleration acts as a retarding force against the direction of the object's motion.

Answer:

1. For a person speeding up: Draw dots at equal - time intervals with increasing - length velocity vectors in the direction of motion.
2. For a person slowing down: Draw dots at equal - time intervals with decreasing - length velocity vectors in the direction of motion.
3. Increasing lengths of velocity vectors indicate speeding up, decreasing lengths indicate slowing down.
4. Two main ideas about acceleration direction: Acceleration in the same direction as velocity causes speeding up; acceleration in the opposite direction of velocity causes slowing down.
5. If velocity and acceleration vectors have opposite signs, the object is slowing down.