The phrase “constant” refers to a state of being stable. What happens when an object’s velocity remains constant? Let’s look at a constant velocity vs. time graph to see what we are talking about.
When a body or object moves at a constant velocity, the constant velocity vs time graph will have no slope. And because velocity remains constant, i.e., it does not change even when time does, there will be no acceleration.
Velocity vs Time Graph:
The velocity of an object or body is nothing but its speed in a particular direction. It means that if two objects or bodies are moving at the same speed but not in the same direction, their velocities will differ.
In the velocity vs time graph, there will be time on the horizontal axis (X-axis) as it is the independent variable. At the same time, on the vertical axis (Y-axis), there will be the object’s velocity as it is time dependent. The velocity vs. time graph is the one that is used to compare how velocity is changing with time. Moreover, using this graph, velocity and its direction of motion, acceleration of an object, and displacement of an object can be found. The slope of the line in the velocity vs time graph will give us the object’s acceleration. The area under that line, on the other hand, will give us the object’s displacement.
Meaning of the slope of the velocity vs. time graph:
In the velocity vs time graph, the slope of the graph gives us acceleration. As we know, if we divide the change in the y-axis to change in the x-axis, it gives us the slope of the graph. As a result, we can write:
We now know that velocity is measured on the y axis, and time is measured on the x axis. As a result of plugging in the y axis and x axis values, we get:
However, dividing the change in velocity by the passage of time yields the value of acceleration. As a result, by looking at the slope of the velocity vs time graph, one can calculate the acceleration. Thus, we can write:
Slope = Acceleration a
When the slope is steeper, its value is higher, so the acceleration is greater. And when the slope is less steep, or we might say shallower, its value is less, so the acceleration is lower.
The meaning of the shape of velocity vs. time graph:
The slope of the graph not only gives the magnitude of acceleration but also tells us how the object is accelerating, i.e., if it is increasing, decreasing, or not accelerating. If the graph has a positive slope, it will also have a positive acceleration. Similarly, if the slope of the graph is negative, it means acceleration is also negative. Lastly, if the graph has no slope or zero slope, the object is not accelerating or has zero acceleration.
To further grasp positive, negative, and zero acceleration, consider the example of boating. The boat is initially stationary on the riverbank. A group of folks decided to take a river trip by boat after some time had passed. As a result, turning on the motor increases the boat’s velocity, and the boat begins to move. The boat is now going at a consistent speed as they approach the middle of the river. They slowed down and then finally came to a halt when they noticed familiar faces on another boat. They restart the boat after some conversation time. This is how the velocity vs. time graph for the entire scenario will look:
If we analyze the graph, we can observe that the boat has no velocity because it is standing on the river bank. As people start the boat’s engine, the velocity increases with time. As a result, its slope will be positive, so its acceleration will be positive. When the boat is moving with constant speed, the graph will be a straight line, and thus it will have no acceleration. After that, as the boat slows down and comes to a halt, its slope will be negative and thus will have negative acceleration, which is also called deceleration.
If you want to know how to find acceleration in the velocity-time graph, go through this article. Let us now focus on the constant velocity vs time graph, which is the primary goal of this article.
Constant Velocity vs Time Graph:
In each time interval, if a body or the object is traveling the same distance in the same direction, then we can say that its velocity is constant. Because velocity does not change with time, the plot of the constant velocity vs. time graph will be a horizontal line parallel to the x axis or the time axis. The line on the graph has no slope because it is horizontal. As a result, we can conclude that the object which is moving with constant velocity has no acceleration.
Consider a car is moving in the east direction with a constant velocity of 7 m/s, i.e., in each second, it travels the distance of 7 m.
If the velocity vs. time graph is plotted for the given data of the car, then the graph will look like the following.
We can observe that because the motion of the car is continuous, the graph of velocity vs. time is a horizontal line. As we know, the horizontal line has no slope; hence there is no acceleration. It can be proved mathematically as follows:
∴ a = 0 m/s2
Frequently Asked Questions (FAQs):
Q: How can you tell when velocity is constant of a velocity time graph?
Ans: The slope of the velocity vs time graph reveals information regarding velocity and acceleration.
Consider an object moving with any velocity and plot the velocity vs. time graph to know its motion. If an object moves at a constant velocity, it shows that there is no change in velocity with time. Thus the graph has no slope. It means if the graph of velocity vs. time is a horizontal line, then we can say that its velocity is constant.
Q: If the object is not accelerating, does it mean that it is stable?
Ans: The object is said to be accelerating if its velocity keeps on changing with time.
The term “stable” refers to an object that has no velocity and consequently no acceleration. Furthermore, if an object moves at a constant velocity (one that does not change over time), it will not accelerate. As a result, we can conclude that if the acceleration is zero, it is not necessarily stable; it can be traveling at a constant velocity.
Q: How can an object with zero acceleration move?
Ans: An object or body can move only if it is under the influence of force.
As per Newton’s second law, if the acceleration of an object or body is zero, it means there is no net force acting on it. The net force is zero means the opposite force acting on an object or body cancels each other. As a result, we can say that an object or a body can move even without acceleration.
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