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An object is moving along the X axis with position as a function of time given by x=x(t)x=x(t).point oo is at x=0x=0. The object is definitely moving toward oo when a) dx/dtdx/dt smaller than zero b) dx/dtdx/dt greater than zero c) dx2/dtdx2/dt smaller than zero d) dx2/dtdx2/dt greater than zero?
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An object is moving along the X axis with position as a function of ti...
Answer:
In order to determine if an object is moving towards positive infinity (oo) or negative infinity (-oo), we need to analyze the behavior of its velocity and acceleration.
Velocity and Acceleration:
Velocity is the rate of change of position with respect to time, given by dx/dt. Acceleration, on the other hand, is the rate of change of velocity with respect to time, given by d^2x/dt^2.
Relationship between Velocity, Acceleration, and Motion:
By analyzing the signs of velocity and acceleration, we can determine the direction of the object's motion:
1. If both velocity and acceleration are positive, the object is moving towards positive infinity (oo).
2. If both velocity and acceleration are negative, the object is moving towards negative infinity (-oo).
3. If velocity is positive and acceleration is negative, the object is slowing down and moving towards positive infinity (oo).
4. If velocity is negative and acceleration is positive, the object is slowing down and moving towards negative infinity (-oo).
Analysis:
Given that the position of the object is x(t), we need to analyze the signs of dx/dt and d^2x/dt^2 to determine if the object is moving towards positive infinity (oo) or negative infinity (-oo).
1. dx/dt:
- If dx/dt is positive, it means the object is moving in the positive direction along the X-axis.
- If dx/dt is negative, it means the object is moving in the negative direction along the X-axis.
2. d^2x/dt^2:
- If d^2x/dt^2 is positive, it means the object is accelerating in the positive direction.
- If d^2x/dt^2 is negative, it means the object is accelerating in the negative direction.
Answer Explanation:
Based on the given information, we can conclude the following:
- If dx/dt is smaller than zero (negative velocity), the object is moving towards negative infinity (-oo).
- If dx/dt is greater than zero (positive velocity), the object is moving towards positive infinity (oo).
- The value of d^2x/dt^2 does not provide any information regarding the direction of the object's motion. It only indicates whether the object is accelerating positively or negatively.
Therefore, the correct answer is a) dx/dt smaller than zero as it indicates that the object is moving towards negative infinity (-oo).
In order to determine if an object is moving towards positive infinity (oo) or negative infinity (-oo), we need to analyze the behavior of its velocity and acceleration.
Velocity and Acceleration:
Velocity is the rate of change of position with respect to time, given by dx/dt. Acceleration, on the other hand, is the rate of change of velocity with respect to time, given by d^2x/dt^2.
Relationship between Velocity, Acceleration, and Motion:
By analyzing the signs of velocity and acceleration, we can determine the direction of the object's motion:
1. If both velocity and acceleration are positive, the object is moving towards positive infinity (oo).
2. If both velocity and acceleration are negative, the object is moving towards negative infinity (-oo).
3. If velocity is positive and acceleration is negative, the object is slowing down and moving towards positive infinity (oo).
4. If velocity is negative and acceleration is positive, the object is slowing down and moving towards negative infinity (-oo).
Analysis:
Given that the position of the object is x(t), we need to analyze the signs of dx/dt and d^2x/dt^2 to determine if the object is moving towards positive infinity (oo) or negative infinity (-oo).
1. dx/dt:
- If dx/dt is positive, it means the object is moving in the positive direction along the X-axis.
- If dx/dt is negative, it means the object is moving in the negative direction along the X-axis.
2. d^2x/dt^2:
- If d^2x/dt^2 is positive, it means the object is accelerating in the positive direction.
- If d^2x/dt^2 is negative, it means the object is accelerating in the negative direction.
Answer Explanation:
Based on the given information, we can conclude the following:
- If dx/dt is smaller than zero (negative velocity), the object is moving towards negative infinity (-oo).
- If dx/dt is greater than zero (positive velocity), the object is moving towards positive infinity (oo).
- The value of d^2x/dt^2 does not provide any information regarding the direction of the object's motion. It only indicates whether the object is accelerating positively or negatively.
Therefore, the correct answer is a) dx/dt smaller than zero as it indicates that the object is moving towards negative infinity (-oo).
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An object is moving along the X axis with position as a function of time given by x=x(t)x=x(t).point oo is at x=0x=0. The object is definitely moving toward oo when a) dx/dtdx/dt smaller than zero b) dx/dtdx/dt greater than zero c) dx2/dtdx2/dt smaller than zero d) dx2/dtdx2/dt greater than zero?
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