Question

If the acceleration of an object is zero and its velocity is nonzero, what can you say about the motion of the object? Sketch velocity versus time and acceleration versus time graphs for your explanation.

Short answer

Answer: An object with zero acceleration and nonzero velocity exhibits motion in a straight line at a constant speed. The velocity vs. time graph is a horizontal line parallel to the time axis at the constant velocity value, and the acceleration vs. time graph is a horizontal line along the acceleration axis (a = 0).

Step-by-step solution

Identify the Given Information

We are given that the acceleration of the object is zero (a = 0) and the object's velocity is nonzero (v ≠ 0).

Understand the Motion Characteristics

Since the acceleration is zero, it means that the object's velocity remains constant, as there is no force acting on it to change its velocity. The constant nonzero velocity implies that the object is moving in a straight line at a constant speed.

Sketch the Velocity versus Time Graph

To sketch the velocity vs. time graph, plot velocity on the vertical axis and time on the horizontal axis. Since the velocity is constant, the graph will be a horizontal line parallel to the time axis, at the constant velocity value.

Sketch the Acceleration versus Time Graph

Similarly, to sketch the acceleration vs. time graph, plot acceleration on the vertical axis and time on the horizontal axis. Since the acceleration is zero, the graph will be a horizontal line on the acceleration axis (a = 0), parallel to the time axis. In conclusion, an object with zero acceleration and nonzero velocity has a constant velocity and moves in a straight line. The velocity vs. time graph is a horizontal line parallel to the time axis at the constant velocity value, and the acceleration vs. time graph is a horizontal line along the acceleration axis (a = 0).

Key concepts

Understanding Constant Velocity

When we talk about an object moving with constant velocity, we are referring to motion where the speed and direction of the object do not change over time. This means the object covers equal distances in equal intervals of time, irrespective of how long it moves. In the exercise presented, a constant nonzero velocity indicates that the object is travelling at a steady pace; it's neither speeding up nor slowing down.

The concept of constant velocity is crucial in understanding motion because it is one of the simplest forms of motion. It's what happens when an object moves in a straight line without any external forces accelerating or decelerating it. For instance, when you slide a hockey puck across a frictionless ice surface, it will move with constant velocity until acted on by another force.

Interpreting a Velocity-Time Graph

A velocity-time graph is a powerful tool that visually represents an object's motion over time. On this type of graph, time is usually plotted on the horizontal axis (x-axis), and velocity is plotted on the vertical axis (y-axis).

The shape and slope of the line on a velocity-time graph can tell you a great deal about the object's motion. For an object moving with constant velocity, the graph is a straight horizontal line. This horizontal line means that the velocity remains unchanged regardless of the time elapsed. One key feature here is the line's slope — or rather, the lack of it. A flat, horizontal line translates to a slope of zero, which correlates with no acceleration ('a' being the slope of the velocity-time curve).

For students, it's important to note that the height of the line above the time axis indicates the magnitude of the velocity. If the line were below the time axis, this would represent motion in the opposite direction, also at constant velocity.

Acceleration-Time Graph Essentials

An acceleration-time graph illustrates how an object’s acceleration changes over time. On these graphs, time is still on the x-axis, while acceleration is mapped onto the y-axis. For an object with constant velocity – meaning, no change in speed or direction – the acceleration is zero. This is depicted in the graph as a straight line running parallel to the time axis, right at the zero on the acceleration axis.

Now, any deviation from this zero line would mean acceleration is occurring - the object is speeding up or slowing down. If the line trends upward, away from zero, the object is speeding up. Conversely, a line trending downward indicates slowing down (deceleration).

From an educational standpoint, it’s crucial for students to compare acceleration-time graphs with velocity-time graphs because it provides a more comprehensive understanding of an object's motion. Recognizing that a flat acceleration-time graph corresponds to a straight, horizontal velocity-time graph is a foundational concept in kinematics.