What Is Constant In Velocity Time Graph: Detailed Facts

In this article, we will learn what is constant in velocity time graph with detailed facts.

If the amount of shift of the position of the object in a specific time duration is consistent, then the velocity of that object will be sustained over the duration of time. If the rate of velocity is persistent then the acceleration is constant.

What is constant velocity on a graph?

If the displacement of the object is congruous and fixed for a certain period of time, then the velocity is consistent and hence, the acceleration will be nil.

If the position of the object accelerating in a particular direction changes at a fixed rate for all the time intervals, then the slope of the position-time graph which is equal to the velocity of the object will stay constant.

Consider the following Displacement-Time Graph. The slope of the graph gives the velocity of the object as the velocity is the ratio of displacement and the time interval.

The velocity between any two points on the slope of a graph will be found the same on calculating. Hence the object is said to have a constant velocity.

Let us see how to calculate the constant velocity on the graph.

Read more on How To Find Acceleration In Velocity Time Graph: Problems And Examples.

Plot the graph for the above data, and calculate the velocity of the object at different time intervals.

Solution: The displacement v/s time graph for the above data is plotted below.

The slope of a graph between point (2,4) and (6,12) is

Slope1=V1=x2-x1/t2-t1

={12-4}/{6-2}=2m/s

The slope of a graph between points (4,8) and (8,16),

Slope2=V2=x2-x1/t2-t1

={16-8}/{8-4}=2m/s

The slope of a graph between points (6,12) and (10,20),

Slope3=V3 = x2-x1/t2-t1

={20-12}/{10-6}={8}/{4}=2m/s

The slope of a graph between points (4,8) and (10,20),

Slope4=V4=x2-x1/t2-t1

={20-8}/{10-4}={12}/{6}=2m/s

We can see that,

V1=V2=V3=V4

This implies that the slope of the graph is at the same altitude and hence the velocity of the object is found constant.

Velocity-Time Graph

“The velocity is defined as the rate of change in the position of the object with respect to time.”

The alternating velocity with a variation of time results in an increase or decrease in the acceleration of the object. The slope of the velocity-time graph, that is y-coordinates divided by the x-coordinates will give the acceleration of the object.

The graph of velocity v/s time is as below.

If the rate of displacement increases at a fixed rate, then the velocity will elevate accordingly at an enduring rate, and hence the acceleration will remain unvaried.

If the velocity remains constant for all the time duration, the acceleration of the object will be zero. The same is shown in the below graph.

The change in the position of the object is consistent and occurs in the same given interval of time, then we will have the constant velocity and hence the acceleration will be zero.

Read more on Zero Average Velocity: What, How, When, Examples And Problems.

Now suppose the object is decelerating with time, then we will have negative acceleration.

If the rate of change in the velocity of the decelerating object is the same then the acceleration will be negative and constant.

As the decelerating object will cover less and less distance with proceeding time, the velocity of the object will keep on decreasing. The slope measure will be found negative; this implies that the acceleration is negative.

What is Constantly Variable on the Velocity-Time Graph?

If the displacement is persistent, then velocity is constant. If the rate of change velocity is sustained then the acceleration is constant.

The displacement in the position of the object is constantly varying and ofcourse the time is constantly varying and is irreversible.

If there is no displacement of the object then it is evident that the velocity of the object will be zero.

Read more on 17+ Constant Velocity Example: Detailed Explanation And Facts.

What is not Constant in Velocity-Time Graph?

The time is undoubtedly a variable quantity in the velocity-time graph.

If the displacement of the object is variable in a fixed time interval, then the velocity and hence the acceleration of the object is not constant.

The velocity of the object is also varying with time and therefore the acceleration. Hence, displacement, velocity, acceleration, and time are variables.

When does the velocity of the object is constant?

The object in a uniform rectilinear motion has constant velocity.

When the object elapses equal distance in a fixed duration of time, then the velocity is sustained by the object.

The object will be in a uniform rectilinear motion unless some external forces act upon the object to accelerate or resist the motion of the object. This is stated in Newton’s First Law of Motion, also called a Law of Inertia; according to which, “There must be some external agency or source to cause the change in the motion of the object or to set the object into motion.”

Read more on How To Find Velocity With Height And Distance:Different Approaches,Problems,Examples.

Example 1: A girl goes to the shop which is 100 meters away from her house and returns back to the home in 5 minutes. The walking speed of a girl is 1m/s.Plot the velocity time graph. Determine what is constant in velocity time graph.

Given: V=1m/s

Distance travelled x=100m

Time t=5min=300 seconds

Time taken to cover a distance of 100m by a girl is

t=x/v

={100}/{1}=100seconds

Hence, the total time in walking to go to the shop and to return back to the home is 200 seconds.

A girl spends 100 seconds in the shop in between. Hence, the velocity-time graph will look like the one given below.

The velocity of a girl between the time intervals 100-200 seconds is zero, as she was in the shop during that time. For rest of the time, the velocity of the girl is 1m/s. The acceleration is zero, as there is no change in speed. The position of a girl before and after is the same.

Example 2: A car is accelerating at a rate of 2km/h. The velocity of the car is 40km/h. What is the final velocity of the car after 2 hours?

Given: a=2km/h

V1=40km/h

T=2 hours

The acceleration of the object is the given as

a=v2-v1/t2-t1

For a car,

2km/h=v2-40km/hr/2h

4=v2-40km

v2=44km/h

The velocity of a car after 2 hours is 44 km/h.

Is acceleration constant in the velocity-time graph?

The y-axis represents velocity and the x-axis denotes time, hence the slope of the velocity-time graph gives acceleration.

If the velocity increases at a consistent rate then the slope of the graph is found to be constant.

Is the Velocity of the object constant in the velocity-time graph?

If the velocity is constant then the graph of velocity v/s time will give the straight line making a point on the y-axis.

If the rate of change in the position of the object is enduring for a duration of time then the velocity is sustained by the object.

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