Constant Acceleration Graph Velocity Vs Time: Detailed Insights

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In this article, we will study Constant Acceleration Graph Velocity Vs time, which is one of the essential aspects of finding the value of acceleration.

As the term constant indicates steadiness, the constant acceleration graph velocity vs time indicates that the acceleration remains constant throughout the motion, only we can find the change in velocity of a body for a certain period by measuring the slope of the plotted curve the V-T graph.

Now let us focus on different aspects of constant acceleration graph velocity vs time, which is the main focus.

What does constant acceleration look like on a velocity vs time graph

The graph of constant acceleration will be linear.

The term constant indicates that there will be no change in acceleration during a particular motion. If the object undergoes this type of acceleration, then the graph plotted will be linear along with slope; these curves are used to find out the value of only variable velocity.

Now let us know about velocity and constant acceleration relation.

What happens to the velocity at constant acceleration

It is known that if the body is accelerating, there is a change in velocity.

  • The accelerating body changes the velocity by an equal amount for each second. It is known to be constant acceleration since velocity changes by an equal amount for a period. Should not compare it with a body having a constant velocity.
  • If we consider a V-T graph, this acceleration is calculated by knowing the slope of the line. If that line is horizontal, that velocity will be constant, and the acceleration will be zero.

It is time to study the graph of constant acceleration.

To know about how to find average velocity on A-T graph check here.

How to know if a graph has constant acceleration

We can interpret the velocity-time or V-T graph by seeing the shape of the curve on its graph.

  • If the V-T graph has a parabolic position curve, it has constant acceleration.
  • It is referred to as a constant acceleration graph.
  • It is further obtained when constant acceleration indicates the continuous change in velocity of a motion.
  • When plotted, the graph will have a steady increase in slope.
  • Constant also ensures that the V-T graph has a constant slope.

The constant acceleration may be straight or parabolic, depending on the values.

How do you interpret an acceleration vs time graph

We can measure the value of change in velocity from the acceleration vs time graph.

When we use the values of observed motion and plot it on a constant acceleration graph vs time, the area under the curve obtained tell about the change in velocity of an object. In other words, we can say that area under the curve for a period will be equal to the velocity change during that interval.

The A-T graph is meant for finding out the velocity change.

How do you graph velocity vs time

There are two possibilities to plot a V-T graph that are summarized below.

  • When the values are plotted on a V-T graph, there will be two types of motion that are classified as constant and variable velocity.
  • The slope of the variable velocity vs time graph gives acceleration. It indicates that the slope at a certain period indicates the acceleration value of the body at that point.
  • If the slope is sharp or steep, the body will have rapid variable velocity.
  • If the slope is shallow, then there will be constant velocity.
  • The other two cases are that if the slope is positive and upwards, then acceleration is positive.
  • If the V-T graph slope value is negative and plotted downwards, the acceleration will be negative. The following image can be an example for motion.
constant acceleration graph velocity vs time
Image credit:
Pixabay free images

Now let us get some information regarding the constant acceleration graph vs time.

Significant cases of Constant acceleration graph velocity vs time

The three essential cases regarding acceleration graph velocity vs time are summarized below.

Case 1: V-T graphs with constant velocity for the case of zero acceleration

  • In a V-T graph, the y-axis signifies velocity, and the x-axis denotes time.
  • From the graph shown below, we can interpret that V is constant in the whole time interval.
  • Even though the time changes, the velocity will be constant at each graph point.
  • Here the initial velocity is positive because we get a different graph when we choose negative initial velocity.
  • Example: Acceleration of an object is zero, and velocity is constant at the rate 6m/s at t=0, then it remains constant throughout the interval.
constant acceleration graph velocity vs time
Image: zero acceleration

Case 2: Constant acceleration graph velocity vs time

Suppose the acceleration and constant, in other words, will be positive, and the initial V is zero. In that case, the velocity of the object increase and we get a linear curve of values when calculated with the help of the following equation.

V = u + at

Here u = 0, then the above equation becomes

V = a * t

constant acceleration graph velocity vs time
Image: Constant acceleration

As shown below, the area’s slope under the graph will measure the magnitude of acceleration.

Case 3: V-T graphs with increasing acceleration

When there is an increase in acceleration, along with time being, the V-T graph obtained will be a curve that can be measured using the formula as shown below,

V = u + (a * t)

Here u = 0, then the above equation becomes

V = a * t

  • We know that acceleration is a function of time; this is why we obtain a curve on the V-T graph.
  • It was only about the increase in acceleration; the deceleration graph will be different from the positive acceleration vs time graph.
  • For example, if a body’s acceleration is a function of t and the initial velocity U=0, the graph will be a curve. The slope of the V-T graph at any instant point of the period gives the acceleration at that time.
constant acceleration graph velocity vs time
Image : Increase in acceleration

Since the acceleration increases continuously with t, the magnitude of its slope will also increase.

Frequently Asked Questions | FAQs

What does the area under a velocity-time graph indicate?

The area we get when we plot the velocity-time graph is a change of position of a body.

When we want to calculate the acceleration on a velocity-time graph, we plot its values. Hereafter plotting the values, we get a specific area under the graph that signifies the displacement that can even be known as a change in position of a body when it is in motion.

What is the slope of the velocity-time graph?

We know that we can calculate acceleration value from the typical velocity-time graph.

When we plot a velocity vs time graph, we will find the value of the acceleration of a body travelling on a path; that is why the slope of the V-T graph represents an acceleration of a body. When we calculate the slope at a particular time, it indicates the acceleration of the body at that point.

How can we interpret an acceleration time graph?

We can interpret an acceleration vs time graph by finding the area under the plotted graph.

The area on the plotted acceleration time graph tells about the change in velocity of the body in motion at a particular period. From this, we can say that area under the curve of the A-T graph is approximately equal to the velocity change of the body.

How do you find out that a graph has constant velocity?

You must see many Velocity time graphs to interpret its values.

If you consider any one of the V-T graphs, and if it is a flat line or horizontal line, we can consider that it has constant velocity. If the graph is other than horizontal, then the velocity is variable, and if you consider an A-T graph and it will be zero, then even in this case, there is constant velocity.

What happens to velocity when the acceleration is constant?

Velocity will not be constant when the acceleration is constant.

In a particular example of motion, if the acceleration of the motion is constant, then there will be no constant velocity because the constant quantity per second will alter the velocity of an object in a specific motion.

How does velocity change with constant acceleration?

There will be a change in velocity when the body moves with constant acceleration.

If a body undergoes constant acceleration, then there will be some constant change in that body’s velocity. If both velocity and acceleration are in the same direction, then the trajectory of this graph will be similar to the graph plotted for no acceleration.

How can you interpret that acceleration is constant from a velocity-time graph?

We can interpret the value of acceleration by observing the type of curve on the graph.

When a body undergoes constant acceleration, the graph will be linear, i.e., straight and sloped. These lines on the V-T graphs represents the change in velocity during motion, but not in the case of constant acceleration and deceleration.

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