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Question

A ball is thrown vertically upwards.  Which of the following graphs correctly represents the variation of acceleration with time during its upward motion (neglecting air resistance)?

NAGA SAI · Accepted Answer

## CORE INFORMATION
✓ **Answer**: A
## CONCEPT FRAMEWORK
 **Primary Concept**: Kinematics, particularly projectile motion under constant gravitational acceleration.
 **Related Topics**: Acceleration due to gravity, free fall.
 **Prerequisites**: Understanding of vectors, graphs, and the concept of acceleration.
## SOLUTION PATHWAY
**Given Information**:
A ball is thrown vertically upwards. Air resistance is negligible.
**Method & Steps**:
1. Analyze the forces acting on the ball.
  Reasoning: The only force acting on the ball (neglecting air resistance) is gravity, which acts downwards.  This force causes a constant downward acceleration.
  Formula/Rule: $F = ma$, where $F$ is the force, $m$ is the mass, and $a$ is the acceleration.  In this case, $F = mg$, where $g$ is the acceleration due to gravity (approximately 9.8 m/s² downwards).
2. Determine the acceleration.
  Working: Since the force of gravity is constant, the acceleration due to gravity is also constant.  The direction of the acceleration is downwards, which we can represent as negative.
  Key Point: The acceleration remains constant throughout the upward motion, even though the velocity changes.
3. Represent the acceleration graphically.
  Result: A straight horizontal line at -9.8 m/s². This represents a constant negative acceleration.
  Verification: The graph should reflect the constant downward acceleration due to gravity.
 ## OPTION ANALYSIS
A ✓: A straight horizontal line at -9.8 m/s² correctly represents the constant downward acceleration due to gravity. 
B :x: A straight line with a negative slope would imply that the acceleration is changing over time, which is incorrect in this case (neglecting air resistance).
C :x: A straight line with a positive slope would imply an upward acceleration, which is opposite to the direction of gravity.
D :x: A parabolic curve would represent a changing acceleration, which is not the case here.
 ## LEARNING AIDS
 **Common Mistakes**:
  1.Confusing velocity and acceleration: Students might mistakenly think that the velocity graph is being asked for, which would be a straight line with a negative slope.
  How to avoid: Carefully read the question to determine whether it is asking about velocity or acceleration.
  2.Ignoring the direction of acceleration: Students might represent the acceleration as positive, forgetting that gravity acts downwards.
  How to avoid:  Remember to assign a negative sign to the acceleration due to gravity when it acts downwards.
 **Quick Tips**:
  1.Remember that the acceleration due to gravity is constant near the Earth's surface (neglecting air resistance).
  2.Draw a free-body diagram to visualize the forces acting on the object.

NAGA SAI · Answer

The correct Option is "A straight horizontal line at -9.8 m/s²"

NAGA SAI · Answer

A straight line with a negative slope

NAGA SAI · Answer

A straight line with a positive slope

NAGA SAI · Answer

A parabolic curve opening downwards

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