A ball is thrown vertically upward into the air. Neglecting air resistance, which of the following physical quantities does not change during its entire motion up and down?

Introduction / Context:

This question tests understanding of motion under gravity. When a ball is thrown vertically upward, it rises, slows down, momentarily comes to rest at the top, and then falls back down. The behaviour of speed, potential energy, distance from the ground, and acceleration during this motion is a key topic in kinematics and helps students apply Newton laws of motion to real situations.

Given Data / Assumptions:

• A ball is thrown vertically upward from near the Earth surface.
• Air resistance is neglected for simplicity.
• The only significant force during the motion is the gravitational force acting downward.
• We are asked which quantity does not change throughout the motion up and down.

Concept / Approach:

Near the Earth surface, and neglecting air resistance, the acceleration due to gravity has a constant magnitude g directed downwards. As the ball goes up, its speed decreases due to this downward acceleration. Its height above the ground increases, so its gravitational potential energy increases. On the way down, the reverse happens. However, at every instant during the flight, the gravitational acceleration is the same in magnitude and direction. Thus, acceleration remains constant, while speed, potential energy, and distance from the ground all change with time.

Step-by-Step Solution:

Verification / Alternative check:

The standard equations of motion for constant acceleration, such as v = u + a t and s = u t + (1/2) a t^2, are used to describe freely falling bodies and vertical throws. In these equations, acceleration a is constant and equal to minus g for upward motion when upward is taken as positive. Experimental measurements using motion sensors also show that the acceleration magnitude remains roughly constant near the Earth surface, confirming that acceleration is unchanged while other quantities vary.

Why Other Options Are Wrong:

• Speed: Speed decreases on the way up, becomes zero at the top, and increases on the way down, so it clearly changes.
• Potential energy: As height changes, gravitational potential energy m g h also changes, increasing and then decreasing.
• Distance from the ground: The vertical distance from the ground is constantly changing, except at two instants when it may pass the same height.

Common Pitfalls:

Many learners instinctively think that at the highest point acceleration becomes zero because the speed is zero. This is incorrect. Acceleration is related to change of velocity, not current velocity value. At the top, the velocity is zero for an instant, but acceleration is still downward, causing the ball to start falling. Confusing velocity with acceleration leads to wrong answers. Remember that in ideal free fall problems near Earth, acceleration due to gravity is treated as constant in magnitude and direction.

Final Answer:

When a ball is thrown vertically upward, the quantity that does not change is the acceleration due to gravity.