What is the acceleration of constant speed?

We know that velocity and acceleration are closely related to each other. As a result, in this article, we will go through how to find acceleration with a constant velocity.

When an object or body is moving and its velocity is constant, then we can say that it is moving with no acceleration. It occurs because constant velocity implies that its magnitude or direction does not change over time.

Let us have a look at how acceleration and velocity are related before we look at how to get acceleration with a constant velocity.

Acceleration:

In general, layman people use the term acceleration when speed is increasing. The accelerator is the part of our bike or car that allows our vehicle to move quickly. However, in physics, acceleration is defined more precisely as the rate at which the velocity of an object or body changes. It means that acceleration is the quantity that tells us how velocity changes over time.

As can be seen, velocity has a complete impact on acceleration. As a result, it is included in the vector quantity, not in a scalar quantity. From this, we can say that for the acceleration, not just its magnitude but also its direction need to be considered.

As a result, if a body or object moves at a constant speed but in a constantly changing direction, the body is said to be accelerated, exactly as in circular motion. Because in a circular motion at every point of the circle, the velocity of the object or body is in the direction of its tangent, which is not the same at every point. As a result, we can claim that circular motion is accelerated motion, even though its magnitude is the same. 

What if the magnitude and direction of velocity remain constant? Let’s have a look at how to find acceleration with a constant velocity.

Motion with a constant velocity:

Consider a body or an object is in motion. If its velocity is not changing with time during the motion, it is said to be constant velocity. Consider a car is crossing the distance of  6 miles per every hour in the same direction, then in this case, it is said to be moving with constant velocity.

How to find acceleration with a constant velocity?

We can find acceleration using either a mathematical technique or a graphical method, depending on whether the velocity is constant or not. Because it is the ratio of change in velocity to change in time, while velocity is constant, the change in velocity is zero, so the acceleration is zero.

Mathematical way to find acceleration:

Acceleration is provided in the form of an equation by:

As a result, if we represent acceleration as a, velocity change as Δv and time change as Δt, we can write:

If we denote vi as the object or body’s initial velocity at time ti and vf as the final velocity at time tf, then the change in velocity v and the change in time t are stated as:

Δv =vf – vi ……….(2)

Δt =tf – ti ………..(3)

Thus, equation (1) can be written as:

However, because the velocity remains constant in this case, time changes, but the velocity does not. As a result, we can write:

vf = vi

∴Δv =vf – vi = 0  ……….(5)

Thus, acceleration

a = 0  ……….(6)

Graphical way to find acceleration:

To find acceleration using the graphical method, we will draw a graph of v vs. t with velocity v on the vertical axis and time t on the horizontal axis. Because velocity is the dependent variable, it is plotted on the vertical axis, while time t is plotted on the horizontal axis. 

You can calculate the value of acceleration by looking at the slope of that graph. 

1. If the slope of the graph is positive, it indicates that velocity is growing over time, and thus the magnitude of the acceleration is also positive. 
2. If the slope of the graph decreases, it signifies that velocity decreases over time, and therefore acceleration is negative, also known as deceleration. 
3. If a graph has no slope, it means it is flat, and this indicates that there is no acceleration or zero acceleration. 

The graphs for positive, negative, and zero acceleration are all shown here.

Assume a car is traveling at a constant speed of 60 m/s. Plotting the graph of v vs. t in this example will be the same as we stated in case 3. Here we can see that as velocity is not changing with time, the graph of v vs. t is horizontal, or we can say flat. Now we know that the slope of velocity v vs. time t graph will give us acceleration a. 

Acceleration a = slope ………..(7)

But here, as the graph is flat, there is no slope, and thus there is no acceleration. 

∴ slope = 0

∴ acceleration a = 0

Let us consider the solved problem related to acceleration with constant velocity.

Problem: Consider a person is walking  5 meters in the same direction every second. What would be the acceleration of that person?

Given parameters:

Distance covered by person d = 5 meters

Time taken to cover this distance t = 1 second

As person is walking in same direction his velocity v = d/t = 5 m/s

To find:

Acceleration of the person = ?

Solution:

Acceleration of the person:

a = Δv / Δt

But as we can see here, the velocity of the person is constant. As a result, Δv =0.

∴ a = 0/1

∴ a = 0 m/s2