Describe what it means (describe the motion) if the acceleration vector has the same direction as the velocity vectors, and what it means if the acceleration vector has the opposite direction as the velocity vectors. Consider all four possibilities and explain what would happen in all cases.
a) velocity vectors positive, acceleration vector positive.
b) velocity vectors positive, acceleration vector negative.
c) velocity vectors negative, acceleration vector negative.
d) velocity vectors negative, acceleration vector positive.
Thanks!
To describe the motion in each case, we need to consider the relationship between the velocity and acceleration vectors. The direction of the vectors will indicate the direction of motion.
a) When the velocity vectors are positive and the acceleration vector is also positive, it means that the object is moving in the same direction as its velocity and is accelerating. This suggests that the object's speed is increasing as it moves.
b) If the velocity vectors are positive and the acceleration vector is negative, it means that the object is still moving in the same direction as its velocity, but its speed is decreasing. This implies that the object is slowing down or decelerating.
c) When both the velocity vectors and the acceleration vector are negative, it indicates that the object is moving in the opposite direction as its velocity vectors and is accelerating. This means that the object is speeding up while moving in the opposite direction from where it was previously moving.
d) Finally, if the velocity vectors are negative and the acceleration vector is positive, it means that the object is moving in the opposite direction as its velocity and is decelerating. This implies that the object is slowing down while moving in the opposite direction.
In summary:
a) Positive velocity vectors and positive acceleration vectors indicate the object is moving in the same direction, speeding up.
b) Positive velocity vectors and negative acceleration vectors indicate the object is moving in the same direction, slowing down.
c) Negative velocity vectors and negative acceleration vectors indicate the object is moving in the opposite direction, speeding up.
d) Negative velocity vectors and positive acceleration vectors indicate the object is moving in the opposite direction, slowing down.
These interpretations rely on the assumption that velocity vectors are positive when the object is moving in one direction and negative when it is moving in the opposite direction. The acceleration vector's sign, either positive or negative, determines if the object is accelerating or decelerating.