# Constant acceleration graph: what, how, examples - (2023)

The movement of an object can be described with the help of a graphical representation. The graph of position time, velocity time, and acceleration time is commonly used to describe motion.

It is said that a body only accelerates when the speed of the body changes. Ochange in speedover time can be plotted on a graph to describe movement. Acceleration can also be plotted in a similar way. In this post, we will know how to draw constant acceleration diagram in different aspects.

## What is a constant acceleration graph?

Constant acceleration means when the rate of change of a body does not change much in a given time interval. In general, the acceleration of a body can be represented by the velocity-time diagram. The slope of the v-t diagram indicates the acceleration.

Motion of a body in a straight line with uniform acceleration is commonly referred to as constant acceleration. A non-zero uniformaccelerationa body moving in the plane can be graphed; This graph is known as a constant acceleration graph.

If the velocity of the moving body is constant, then we get zero acceleration.

Suppose a car is moving at a certain speed and increases its speed by 25 m/s in the next 5 minutes within the 5 minute time interval. In this case, the car needs to increase its speed by 25 m/s; In this case, the acceleration of the car is called a constant.

If we graph the increase in velocity over time, we get the acceleration from the slope of the graph, which represents constant acceleration.

## How do you know if the acceleration is constant on a graph?

We've already looked at what a graph of constant acceleration means. Can you see from the diagram that the acceleration is constant?

The gradient of the velocity-time diagram indicates the acceleration. By differentiating the slope obtained, we can tell from the graph whether the acceleration is constant or not.

From the graph above, we can calculate the slope as

(Video) Constant Acceleration Graph Example

Slope = AB/BC

In the graph AB = v and BC = t; therefore, the slope can be written as

slope = v/t

If we now derive the given slope equation, we get;

du/dt = 0

The derivative of the slope is zero, which means that the acceleration is constant. If the derivative of the slope has a certain value, the acceleration is not constant.

Now look at the position versus time graph; the slope of local time gives the speed. If the velocity is constant on the position-time diagram, the acceleration on the diagram is also constant.

The slope of the x-t graph can be written as

declive=y/x= x/t

Now differentiate the slope obtained, we get the velocity as

(Video) Constant Acceleration 1 • Displacement and Velocity Time Graphs • Mech1 Ex9A/B • 🚀

dx/dt=v

Differentiating the above equation again, we get

D2x/dt2=dv/dt

But the first order derivative of the velocity gives the acceleration; therefore, the equation can be rewritten as

D2x/dt2=dv/dt=a

This implies that, on a position versus time graph, if the second-order time derivative of distance is constant, then acceleration is constant. Or, in other words, if the derivative of the slope of the position versus time graph is constant, then the acceleration on the x-t graph is constant.

## When is acceleration constant on a graph?

Acceleration is constant on the graph when the speed of the moving object is increasing or decreasing at a constant rate.

If you draw the graph of velocity versus time and the curve you get from the graph is a straight line, the slope is constant throughout the graph. The acceleration is therefore constant on the diagram.

If you plot the position versus time graph, the slope of the graph indicates velocity. SinceChange in speed gives acceleration, then the x-t diagram gives the constant acceleration as shown below.

If the curve obtained by drawing an x-t graph is a parabola, as shown in the figure above, then from the graph we can say the following:

(Video) Acceleration - graphs for motion with constant acceleration

• Between points A and B, x has a negative value. The object starts moving towards the origin, causing the object's velocity to become positive. The slope of the object is positive and therefore the acceleration is positive and it has a constant acceleration.
• At point B, the object hits the origin and x takes on a positive value. In this position, the object gains maximum speed and the speed increases proportionally. Therefore, the acceleration is constant.
• Between points B and C, the value of x increases and the object starts moving to the right of the origin. Thus, the object's velocity decreases at a constant rate and the slope of the graph also decreases, although the acceleration remains constant.

Therefore, from the two examples in the graph above, it is clear that the acceleration is constant when the object's motion follows a straight-line path or a parabolic curve with a change in velocity.

## How to draw constant acceleration?

There are several methods for plotting the constant acceleration graph. Three important ways to represent constant acceleration are:

Now let's discuss how to plot a constant acceleration using these three graphs in sequence.

Position versus time diagram

The position versus time diagram is usually plotted to describe motion and its slope is used to calculate the velocity of a particle.

Since the second-order time derivative ofDistance indicates acceleration, we can plot the constant acceleration graph using the position versus time graph. The start and end position where the object was within the given time interval is used to plot a constant acceleration.

The x-t graph showing the constant acceleration is shown below.

In the graph above, position versus time gives the parabolic curve, increasing velocity and positive acceleration. From the equation of motion, the distance traveled by the body is given by the equation

In the above equation, x is the final position and x0is the starting position of the body.

Using the expression above, the constant acceleration can be plotted on the graph using the change in magnitude of the velocity.

(Video) Constant Acceleration and Graphs of Motion

Speed ​​x time diagram

An object is accelerated uniformlystraight motioncan be plotted using velocity on the vertical axis and time on the horizontal axis.If the velocity increases linearly with successive time intervals, then the acceleration is constant.

The kinematic equation of motion is used for illustration.constant acceleration on v-t diagram.

v = v0+ em

Looking at the graph above, theinitial speed v0Eterminal velocity vwith the given time t form the right triangle that helps to describe the constant acceleration in the diagram.

from the triangle

From the above expression, we can express the change in velocity as;

The above equation gives the change in velocity, whose slope gives the acceleration. The acceleration in the diagram is constant.

Acceleration time diagram

The graph of acceleration time for constant acceleration is a straight line. Acceleration does not change with time.The area covered by the a-t diagram gives the change in velocity.The constant acceleration acceleration time graph is given below.

(Video) GCSE Science Revision Physics "Acceleration"

Acceleration does not change with time to give constant acceleration.

## Example 1) When a person drives the car on a busy road, at first he drives the car with a smooth increase in speed. When he reaches the city limit speed, his speed becomes constant. If he suddenly encounters speed bumps on the road, then his speed will decrease. The v-t diagram for this situation is given below.

From the graph above, we can analyze some facts, for example

• The car starts moving from point A; this point would be the initial speed of the car.
• From point A to B, the velocity increases smoothly over time, and the slope also increases, so the acceleration between A and B is constant.
• Between points B to C the velocity is kept constant and therefore there is no acceleration.
• From point C to D, the speed of the car decreases and the slope decreases, so we get a constantly decreasing acceleration.

## Example 2) The movement of an object is shown in the graph below,

By analyzing the graph above, we can understand things like:

• At point "0", the starting position from which the object starts moving.
• Between points 0 and A we can observe the increase in velocity expressed by the increase in incline when the incline increases steadily with time; the acceleration is constant.
• Between points A and B, the slope decreases, which means the speed decreases. However, the decrease in velocity is constant to observe constant acceleration.
• Between points B and c the slope increases and so we can observe the variation in velocity; therefore, the acceleration between B and C is constant. Between points C and D, the slope is constant, which implies that the velocity of the object is constant. Therefore, there is no acceleration between C and D.

## FAQs

### What is an example of constant acceleration? ›

Constant acceleration is defined as a change in velocity that does not vary over time. If a car increases its velocity by 20 mph in one minute, then another 20 mph the next, its average acceleration remains constant at 20 mph per minute.

How is constant acceleration shown on a graph? ›

Constant acceleration means a horizontal line for the acceleration graph. The acceleration is the slope of the velocity graph. Constant acceleration = constant slope = straight line for the velocity graph.

Does the object have acceleration if they are in constant motion explain your answer with example? ›

Note: All circular motions where the object is moving with constant velocity are a great example of cases where the body will have constant speed but it will be still accelerating since the velocity changes due to a change in direction of the object.

How do you know when acceleration is constant? ›

The rate of change of the velocity of a particle with respect to time is called its acceleration. If the velocity of the particle changes at a constant rate, then this rate is called the constant acceleration.

What are 4 examples of acceleration? ›

A few examples of acceleration are the falling of an apple, the moon orbiting around the earth, or when a car is stopped at the traffic lights. Through these examples, we can understand that when there is a change in the direction of a moving object or an increase or decrease in speed, acceleration occurs.

What happens when an object has a constant acceleration? ›

An object that travels with constant acceleration has a speed that changes by the same amount each second.

How do you show that a graph is constant? ›

Constant: A function is constant, if as x increases (reading from left to right), y stays the same. In plain English, as you look at the graph, from left to right, the graph goes flat (horizontal). The graph has a slope of zero.

How can an object have a constant speed but still accelerate? ›

An object which experiences either a change in the magnitude or the direction of the velocity vector can be said to be accelerating. This explains why an object moving in a circle at constant speed can be said to accelerate - the direction of the velocity changes.

Can the speed of an object be constant but the object be accelerating? ›

If an object is maintaining a uniform circular motion, then at every point of that motion, the velocity of the object varies because it changes its direction, but the speed remains unchanged. Thus, it is possible for an object moving with a constant speed to accelerate.

Can an object move with constant acceleration? ›

Whenever an object is moving with constant acceleration, that objects velocity is changing with a constant rate. Examining the motion of objects moving with constant acceleration can provide us with insight into how certain variables change with respect to other variables.

### Does constant acceleration mean zero acceleration? ›

So, although zero is a constant, zero acceleration is zero acceleration, not constant acceleration.

How do you solve for acceleration? ›

Acceleration (a) is the change in velocity (Δv) over the change in time (Δt), represented by the equation a = Δv/Δt.

What are the types of acceleration with examples? ›

The free-falling of an object is an example of uniform acceleration. Non-uniform acceleration: When an object is traveling with a uniform increase in velocity but not at equal intervals of time is known as non-uniform acceleration. Bus moving or leaving from the bus stop is an example of non-uniform acceleration.

What happens to force at a constant acceleration? ›

As we increase the force on an object the acceleration increases proportionally. Since the mass does not change as the acceleration increases, we can say that force is equal to acceleration. Therefore, if you double the force you double the acceleration.

What is an example of a constant graph? ›

The graph of a constant function is a horizontal line, that is, a line with slope 0.

What is a constant function example with graph? ›

Graphically speaking, a constant function, y = b, has a y-value of b everywhere. This means there is no change in the y value, so the graph stays constantly on y = b, forming a horizontal line. Consider our example of y = 7. The points on this graph all have a y-value of 7.

What is an example of a constant function? ›

In mathematics, a constant function is a function whose (output) value is the same for every input value. For example, the function y(x) = 4 is a constant function because the value of y(x) is 4 regardless of the input value x (see image).

How do you know if an object is moving at constant velocity? ›

An object has constant velocity when both the magnitude and direction of the rate at which such an object is changing its position remain constant. In other words, for an object to have constant velocity its movement has to not change directions over time and the object must have constant speed as well.

Is it possible for something to accelerate but not change its speed? ›

Hence, It is possible for something to accelerate but not change its speed if it moves in a circular path.

Which of the following describes an object moving at constant acceleration? ›

Therefore we can say therefore we can say change in velocity change it in velocity change in velocity occurs at the a curse at the same rate occurs at the same defines defines defiance. Constanta defines constant acceleration. This is the answer.

### What are some examples of objects moving at a constant speed? ›

The angular velocity of the object is constant if the linear velocity of the object remains constant.
• Motion of an object due to Centripetal Force. ...
• Revolution of a moon around the Earth. ...
• A person walking on the street at a constant speed. ...
• Drawing water from a well with the help of a pulley. ...
• A ray of light.

How does constant acceleration affect velocity? ›

A constant acceleration of an object ensures that the velocity of the object is changing continuously with time, and the velocity will not be constant. A constant acceleration, however, means that the velocity will change at a definite rate.

Is it possible for speed to be constant while acceleration is not zero example? ›

Yes, it is possible to have an accelerated motion with constant speed. Let's take an example of a particle moving in a uniform circular motion, it has acceleration because the direction of the motion is changing but it has a constant speed along tangential throughout the motion.

Can you have constant acceleration but zero velocity? ›

When the object is thrown upwards and reaches the maximum height, the velocity of the body becomes zero, but it still accelerates with constant acceleration. The constant acceleration is due to gravity.

What is constant acceleration in real life? ›

Constant acceleration refers to motion where the speed increases by the same amount each second. The most notable and important example is free fall. When an object is thrown or dropped, it experiences a constant acceleration due to gravity, which has a constant value of approximately 10 meters per second squared.

What are 3 examples of acceleration? ›

Some positive acceleration examples are given below:
• Launching a rocket.
• Accelerating a vehicle.
• A free falling object.
• Pedaling a bicycle.
• Rowing a boat.
• Airplane take off.

What are the 3 constant acceleration equations? ›

Solving for Final Velocity from Acceleration and Time

a = v − v 0 t ( constant a ) . a = v − v 0 t ( constant a ) . v = v 0 + a t ( constant a ) . v = v 0 + a t ( constant a ) .

Is 9.8 a constant acceleration? ›

"9.81 meters per second squared" means that objects on Earth will accelerate (or go faster) 9.81 meters every second, if they are in free fall, due to the pull of gravity. Throughout space, gravity actually is constant.

Why do we use constant acceleration? ›

Whenever an object is moving with constant acceleration, that objects velocity is changing with a constant rate. Examining the motion of objects moving with constant acceleration can provide us with insight into how certain variables change with respect to other variables.

What does constant acceleration look like on a distance time graph? ›

If the straight line has a slope, then that indicates the body is changing its velocity at a constant rate, or it means that the body has constant acceleration.

### Is constant speed an example of acceleration? ›

Acceleration is the rate of change of velocity. Usually, acceleration means the speed is changing, but not always. When an object moves in a circular path at a constant speed, it is still accelerating, because the direction of its velocity is changing.

What does acceleration mean example? ›

acceleration, rate at which velocity changes with time, in terms of both speed and direction. A point or an object moving in a straight line is accelerated if it speeds up or slows down. Motion on a circle is accelerated even if the speed is constant, because the direction is continually changing.

What is an example of constant velocity? ›

The simplest type of motion (excluding the trivial case in which the body under investigation remains at rest) consists of motion with constant velocity. This type of motion occurs in everyday life whenever an object slides over a horizontal, low friction surface: e.g., a puck sliding across a hockey rink.

How do you find distance with constant acceleration and time? ›

When acceleration (a) is constant and the initial velocity is zero, we can use the equation - distance, d=1/2*a*t2(t squared) solved for time, t.

What happens to velocity at constant acceleration? ›

A constant acceleration would mean the velocity will change at a constant rate with time.

Does constant acceleration mean 0? ›

So, although zero is a constant, zero acceleration is zero acceleration, not constant acceleration.

What is constant acceleration called? ›

Uniformly Accelerated Motion - Constant Acceleration or Uniform Acceleration | BYJU'S.

Can an object have a constant acceleration? ›

Let's take an example of a particle moving in a uniform circular motion, it has acceleration because the direction of the motion is changing but it has a constant speed along tangential throughout the motion. Yes, it is possible to have constant acceleration and varying speed.

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