How To Find Constant Velocity: Different Approaches And Problem Examples

This article discusses about how to find constant velocity. When the velocity is constant, the acceleration of the object is zero.

When we are considering an object’s speed as well its direction, the combination of both speed and direction forms the velocity of the object. In very simple words, one can say that velocity of an object is the rate at which it changes its displacement while in motion. This article discusses about constant velocity, constant velocity formula and other related topics.

What is velocity?

As we have discussed above, velocity is defined as the rate at which an object travelling in a linear or angular motion changes its displacement. For linear motion, it is called linear velocity and for angular motion it is called as angular velocity.

It can be referred to as the speed of an object with its direction of motion. It should be noted that the magnitude of both speed and velocity can be same in spite of the fact that their meanings are different. One is a scalar which does not have direction associated with it and other is a vector. We shall study about scalar and vector quantities in later sections of this article.

What is acceleration?

Acceleration of an object is defined as the rate at which it changes its velocity while in motion. In simple words, it is a quantity which tells us how fast the velocity of the object is increasing. The units of acceleration are rad/s^2.

It is important to know about the acceleration of the object so that we can calculate the total time the object will take to reach a particular destination. In case of braking, deceleration (negative acceleration) helps us to calculate how much time the vehicle will take to stop. This is essential to avoid the accidents taking place on roads.

What are scalar and vector quantities?

Scalar and vector quantities may be same in magnitude. These quantities are a measure of certain property of the object in motion. 

The only difference between them is that scalar quantities have no direction, they have only numeric values for example temperature. Whereas vector quantities have direction term attached to it. The example of vector quantity is velocity.

What do you mean by displacement?

Displacement is the shortest possible path between two points under consideration. The displacement and distance travelled by an object are two complete things and not the same.

The distance is a measure of total path travelled by an object and the shortest possible path between the two considered points is called as displacement. Numerically, the value of displacement can be smaller or equal to that of distance travelled. When the distance is the shortest possible path then it can be said that displacement and distance are equal.

How to find constant velocity on a graph?

The graph drawn with the help of displacement and time values can be used for finding the velocity of the object. The slope of this graph gives velocity of the object.

When the slope is constant, that is the displacement increases linearly in a straight line with time then it can be said that the object is moving with constant velocity. The magnitude of constant velocity can be calculated by calculating the tan of the angle subtended by the line on the graph with horizontal. It can be shown below-

how to find constant velocity
Image: Displacement time graph with constant slope

The time is represented on the x axis and position of the object is given on the Y axis. Calculating the tan of the angle from the triangle formed. We get velocity equal to tan(theta).

How to find constant velocity from acceleration?

It is defined as the rate at which the velocity of an object changes while in motion. As the velocity varies with time, the value of acceleration also changes. On the other hand, we can say that if there is acceleration then the velocity of the object is changes continuously.

If we want to find the value of constant velocity, then the acceleration has to be zero. Which means the term dv/dt=0. Hence we can say that the change in velocity is zero so the acceleration is zero. As there is absence of acceleration, we cannot find the value constant velocity from acceleration.  

Velocity-time graph

The velocity-time graph is a graph between velocity and time which helps us understand different characteristics of the motion of the object.

The vertical axis represents velocity whereas the horizontal axis represents time. We can use this graph to determine various quantities such as displacement (area under the curve), average velocity and acceleration.

How to find constant velocity on a velocity time graph?

The constant velocity is represented as a straight horizontal line on velocity time graph. Anything except a straight horizontal line on velocity-time graph represents a motion with variable velocity.

Its magnitude can be found by simply observing the value at which the straight horizontal line is drawn. That value is the value of constant velocity. The value of velocity does not changes in a constant velocity motion.The area that lies under this curve represents the displacement of the object. 

Constant velocity example

Below are some examples of objects travelling with constant velocity. These examples are very common and already known to us.

  • A man walking with equal length of footsteps- A man covering equal displacements at equal intervals of time is an example of constant velocity motion.
  • An object falling at terminal velocity- After achieving terminal velocity, the object does not attain any significant speed and that the value of acceleration becomes zero. This case can be considered as a case of constant velocity motion.
  • A train travelling equal displacements in equal intervals of time– The net change in velocity is zero as the train covers equal displacements at equal intervals of time.
  • An aeroplane flying at same speed- Aeroplane travelling at the same speed while cruising covers equal displacements in equal intervals of time, hence it is also an example of constant velocity motion.
  • A fan rotating at same speed– When the regulator of the fan is left untouched, the speed of the fan does not change, this is a case of angular motion and the blades of fan move with constant angular velocity.
  • Revolution of Earth around Sun– Revolution of Earth around Sun is also an example of constant velocity angular motion. It takes exactly 365 days to complete one revolution around Sun.
  • Satellite orbiting the Earth– Every satellite needs to attain a particular value of velocity to maintain its orbit. The value changes during its course correction but the change is negligible. This comes under the tag line of angular motion having constant angular velocity.
  •  A car running at its full speed- When a car attains its full speed, the acceleration value becomes zero which results in a constant velocity motion
  • Speed of light– Speed of light is constant in vacuum and does not change unless there is a change in medium.
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