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If the upward direction is taken as positive what is the sign of velocity and acceleration when a body falls freely from a height.
- a)positive acceleration and negative velocity
- b)positive acceleration and positive velocity
- c)negative acceleration and positive velocity.
- d)negative acceleration and negative velocity
Correct answer is 'D'. Can you explain this answer?
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Verified Answer
If the upward direction is taken as positive what is the sign of veloc...
Both velocity and acceleration are in the downward direction. Thus, they will be considered negative as they are vectors and the upward direction is positive.
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If the upward direction is taken as positive what is the sign of veloc...
The sign convention for velocity and acceleration is determined by the chosen coordinate system. In this case, the upward direction is taken as positive. Let's analyze the motion of a body falling freely from a height using this convention.
1. Initial Conditions:
- The body is at rest when it is dropped from a height.
- The initial velocity is zero.
2. Motion during Free Fall:
- As the body falls freely, it accelerates downwards due to the force of gravity.
- The acceleration remains constant throughout the motion and is equal to the acceleration due to gravity (9.8 m/s^2).
- The velocity of the falling body increases in the downward direction as time progresses.
3. Sign of Velocity:
- Since the upward direction is taken as positive, the velocity of the falling body will be negative.
- This is because the body is moving in the downward direction, opposite to the positive direction.
4. Sign of Acceleration:
- The acceleration due to gravity acts in the downward direction.
- Therefore, the acceleration will also be negative.
- The negative sign indicates that the acceleration is acting in the opposite direction to the positive direction defined by the coordinate system.
5. Final State:
- When the body reaches the ground, its velocity will be at its maximum, which is negative.
- The acceleration remains negative as long as the body is falling.
Hence, it can be concluded that the correct answer is option D: negative acceleration and negative velocity. This is because the body is falling in the negative direction (opposite to the positive direction defined by the coordinate system) and its velocity and acceleration are both negative.
1. Initial Conditions:
- The body is at rest when it is dropped from a height.
- The initial velocity is zero.
2. Motion during Free Fall:
- As the body falls freely, it accelerates downwards due to the force of gravity.
- The acceleration remains constant throughout the motion and is equal to the acceleration due to gravity (9.8 m/s^2).
- The velocity of the falling body increases in the downward direction as time progresses.
3. Sign of Velocity:
- Since the upward direction is taken as positive, the velocity of the falling body will be negative.
- This is because the body is moving in the downward direction, opposite to the positive direction.
4. Sign of Acceleration:
- The acceleration due to gravity acts in the downward direction.
- Therefore, the acceleration will also be negative.
- The negative sign indicates that the acceleration is acting in the opposite direction to the positive direction defined by the coordinate system.
5. Final State:
- When the body reaches the ground, its velocity will be at its maximum, which is negative.
- The acceleration remains negative as long as the body is falling.
Hence, it can be concluded that the correct answer is option D: negative acceleration and negative velocity. This is because the body is falling in the negative direction (opposite to the positive direction defined by the coordinate system) and its velocity and acceleration are both negative.
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If the upward direction is taken as positive what is the sign of veloc...
According to co-ordinate system the values which are towards the right hand side and the ones which are on the upper side are considered positive and the values on the left hand side and downward direction are considered negative and as acceleration due to gravity is in downward direction and velocity is also towards downward direction both are taken as negative
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If the upward direction is taken as positive what is the sign of velocity and acceleration when a body falls freely from a height.a)positive acceleration and negative velocityb)positive acceleration and positive velocityc)negative acceleration and positive velocity.d)negative acceleration and negative velocityCorrect answer is 'D'. Can you explain this answer?
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