Does Constant Acceleration Mean Constant Velocity: Detailed Facts

Constant velocity and constant acceleration are phrases that you could come upon. Does constant acceleration mean constant velocity? Let us have a look at this article to find out the answer.

When an object moves with a constant velocity, it means that the moving object has no acceleration. However, when an object moves with constant acceleration, its velocity changes by a constant amount throughout the same time interval.

Before delving into the answer, it is important to understand what you mean by constant velocity and constant acceleration. Let us have a look at it first.

Constant Velocity:

Velocity is the physical term that gives information about the rate of change of an object or body’s displacement. Thus, if an object changes its displacement from xi to xf over a time interval t, its velocity v may be calculated using the following formula:

Thus, when the distance traveled in one direction is the same during each time interval, then the velocity of an object or body is said to be constant.  

As a result, having a constant velocity does not imply that the object is stable. If a graph of displacement vs time is drawn, it will be parallel to the X axis, the time axis, i.e. a horizontal line as shown in the figure below.

Constant Acceleration:

Acceleration is also the physical term that gives information about the rate of change of an object or body’s velocity. Thus, when a moving object is changing, its speed in one direction is the same during each time interval, then the acceleration of an object or body is said to be constant. Thus, if an object changes its velocity from vi to vf over a time interval t, its acceleration a may be calculated using the following formula:

As a result, same as the constant velocity, having a constant acceleration also does not imply that the object is stable. If a graph of velocity vs time is drawn, it will be parallel to the X axis, the time axis, i.e. a horizontal line as shown in the figure below.

does constant acceleration mean constant velocity

Learn more about the graph of constant velocity vs. time by reading this article.

Does constant acceleration mean constant velocity?

Constant acceleration and constant velocity are two physics expressions that have different meanings.

When anything has constant acceleration, it means that its velocity change is the same in each time interval. It means it is subjected to the same amount of force throughout the motion. As a result, constant acceleration does not imply constant velocity at all.

You might wonder what are the differences between constant velocity and constant acceleration? Let us look at the differences between constant velocity and constant acceleration.

Constant velocity vs Constant acceleration:

Motion with constant velocity and constant acceleration has totally different meanings. The followings are the differences between constant velocity and constant acceleration:

Suppose any object or body is traveling with constant velocity. It means that it continuously travels at the same speed and also in the same direction. If the velocity of an object or body is constant, then its velocity is not changing, and thus, it has no acceleration with time. Consider you are driving on the highway on one way where your speedometer indicates the same speed, then it is said that you are traveling with constant velocity.

Constant acceleration is quite different from constant velocity. Suppose any object or body is moving with constant acceleration. It means that the velocity of an object or body is changing, but the rate at which it is changing is always constant. The best example of constant acceleration is the acceleration due to gravity. 

Consider an object is falling from some height, which happened due to the earth’s gravitational force. If you are considering the earth’s gravitational force, then the gravitational acceleration due to earth has a constant value of 9.8 m/s2. The gravitational force on the moon is 1/6th of that of the earth. Thus, the gravitational acceleration of the moon is also 1/6th of that of the earth, so its value is 1.625 m/s2.

Frequently Asked Questions (FAQs)

Q: Does constant velocity mean no acceleration?

Ans: Acceleration is a physics term that describes the rate at which velocity changes.

When a moving item has constant velocity, it means that time is changing, but its velocity is not. As a result, according to the definition of acceleration, if the object’s velocity does not change, it does not have acceleration. As a result, we might conclude that constant velocity implies no acceleration.

Q: What is the cause of the object’s zero acceleration?

Ans: Zero acceleration term denotes that the velocity of an object or body remains constant across time.

When no net force is exerted on a moving object, the object will continue to move in the same direction and speed, or more accurately, velocity. As a result, given those circumstances, we can say that it has zero acceleration.

Problems of finding velocity and acceleration:

Problem 1: At time t = 25 seconds, a boat is moving at a velocity of 50 m/s, and at time t = 50 seconds, the same boat is moving at a velocity of 100 m/s. Find the constant acceleration by calculating the change in velocity and time.

Given:

Initial time ti = 25 s

Finale time tf = 50 s

At time t1 velocity of a boat vi = 50 m/s

At time t2 velocity of the same boat vf = 100 m/s

To find:

Change in velocity Δv = ?

Time interval Δt = ?

Acceleration a = ?

Solution:

Change in velocity:

Δv = vf – vi = (100 – 50) m/s = 50 m/s

Time interval:

Δt = tf – ti = (50 – 25) s = 25 s

Constant acceleration of the boat:

a = Δv/Δt =(50 m/s) / 25 s 

∴a = 2 m/s2

Thus, the constant acceleration of the boat is 2 m/s2.

Problem 2: Consider a car is moving in the east direction, and in each second, it travels the distance of 7 m. Find its velocity and acceleration.

Given:

Time interval Δt = 1 s

Change in displacement Δx = 7 m

To find:

Velocity v = ?

Acceleration a = ?

Solution:

Velocity of the car:

v = Δx / Δt

∴ v = 7 m / 1 s = 7 m/s

As each second car is traveling a distance of 7 m, we can say that its velocity is constant, and its value is 7 m/s.

Acceleration of the car:

As the car has constant velocity we can say that Δv = 0.

Thus, acceleration of the car a = 0 m/s2.

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