An object that is thrown straight up falls back to Earth....

Name: Problem 19, Chapter 3: University Physics Volume 1
Uploaded: 2020-06-28T03:51:54-08:00
Duration: 1 min 23 s
Channel: Surjit Tewari
Description: An object that is thrown straight up falls back to Earth. This is one-dimensional motion. (a) When is its velocity zero? (b) Does its velocity change direction? (c) Does the acceleration have the same sign on the way up as on the way down?

An object that is thrown straight up falls back to Earth. This is one-dimensional motion. (a) When is its velocity zero? (b) Does its velocity change direction? (c) Does the acceleration have the same sign on the way up as on the way down?

Key Concepts

One-dimensional Motion

One-dimensional motion refers to movement along a straight line, which simplifies the analysis of movement because only one coordinate is needed to describe the position of an object. In problems like projectile motion along a vertical line, the object’s displacement, velocity, and acceleration are all considered along a single axis, making it easier to apply kinematic equations.

Projectile Motion in One Dimension

Although projectile motion can be analyzed in two dimensions, when an object is thrown straight up and falls back down, its motion is confined to a single vertical line. This simplification allows the study of aspects of motion such as the moment when the object reaches its highest point, where its velocity momentarily becomes zero.

Velocity

Velocity is a vector quantity that describes the rate and direction of change in position. In vertical motion problems, velocity plays a crucial role because it changes continuously due to gravitational acceleration. At the peak of its trajectory, the object’s velocity becomes zero before reversing direction, demonstrating the concept of instantaneous velocity.

Acceleration

Acceleration in the context of projectile motion refers to the constant rate of change of velocity. Even when the object’s velocity reaches zero, the acceleration due to gravity remains constant in magnitude and direction. This constant acceleration is a foundational concept in kinematics, indicating that gravitational pull does not change depending on whether the object is moving up or down.

Sign Conventions

Sign conventions are critical when analyzing vector quantities like velocity and acceleration. By assigning positive or negative signs to different directions (typically up as positive and down as negative), it becomes clear how the quantities interact. For instance, even though velocity changes sign when the object reverses direction, the acceleration due to gravity retains the same sign throughout the motion.

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