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  • Velocity and Acceleration of a Projectile: Ball Thrown Upward
    Here's a breakdown of velocity and acceleration when a ball thrown upwards returns to your hand:

    Understanding the Motion

    * Going Up: When you throw the ball upward, its initial velocity is positive (let's say upwards is the positive direction). As the ball travels against gravity, its velocity decreases. This is because gravity is constantly acting downwards, slowing the ball down.

    * At the Highest Point: At the peak of its trajectory, the ball momentarily stops moving upwards. Its velocity is zero at this point.

    * Coming Down: As the ball starts falling back down, its velocity is now negative, increasing in magnitude as gravity accelerates it.

    Velocity and Acceleration

    * Velocity: Velocity is a vector quantity, meaning it has both magnitude (speed) and direction.

    * Going up: Positive velocity, decreasing in magnitude.

    * At the highest point: Zero velocity.

    * Coming down: Negative velocity, increasing in magnitude.

    * Acceleration: Acceleration is the rate of change of velocity. Throughout the entire motion, the ball experiences a constant downward acceleration due to gravity (approximately 9.8 m/s²).

    * Going up, at the highest point, and coming down: Acceleration is always -9.8 m/s² (downward).

    Key Points

    * Constant Acceleration: Even though the velocity changes direction, the acceleration due to gravity remains constant and downward.

    * Velocity and Acceleration Direction: Velocity and acceleration can have opposite directions. When the ball is moving upward, its velocity is positive, but its acceleration is negative (downward).

    * Symmetry: The upward and downward motions of the ball are symmetrical. The time it takes to go up to its highest point is equal to the time it takes to come back down.

    Important Note: This analysis assumes negligible air resistance. In reality, air resistance will slightly affect the ball's motion, making the descent slightly slower than the ascent.

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