What Is Constant Negative Velocity: Why, How, When and Problem Examples

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The article discusses about what is constant negative velocity with some solved problem examples.

The constant negative velocity is defined by values of displacement. If it increases with time, an object drives straight with constant positive velocity. But if it decreases with time, an object drives in reverse or opposite direction with constant negative velocity.  

Since velocity is a vector quantity, it can be positive or negative depending on its direction, determined by its displacement. When no net force applies, an object moves with constant speed in the same direction, either straight or opposite. In the previous article, we have thoroughly discussed about constant positive velocity when an object moves in a straight direction. 

In the displacement time graph plot for the decreasing displacement per unit time for an object moving in the opposite direction, we obtain a straight line vertical slope. The slope starts from a higher displacement value and ends at a lower displacement value, symbolizing the constant negative velocity. 

What is Constant Negative Velocity
What is Constant Negative Velocity
Constant Negative Velocity Slope
Constant Negative Velocity Slope in Displacement Time Graph

The graph also helps us to calculate the value of constant negative velocity from its slope. 

v→ = s2-s1/t2-t1

Read more about How to Calculate Speed from Force and Mass.

Calculate the constant negative velocity of the car from the below displacement vs. time graph. 

Displacement Time Graph
Displacement Time Graph

Given:

From graph,

s1 = 60m

s2 = 0m

t1 = 0sec

t2 = 6sec

To Find:

v→  =?

Formula:

v→ =s2-s1/t2-t1= Δs/Δt (s→)

Solution:

The constant negative velocity of the car is calculated as,

v→= s2-s1/t2-t1

Substituting all values,

v→=0 -60/6-0

v→ = -10

The constant negative velocity of the car is -10m/s.

Read more about Horizontal Velocity.

How is Constant Velocity Negative?

The constant velocity is negative as an object’s displacement decreases with time.  

The constant velocity becomes negative when the object’s displacement decreases with time. It occurs because an object moves in the opposite direction after traveling a certain distance straight with constant positive velocity. 

Since there is no external force, an object cannot accelerate in any other direction, and it moves with a constant velocity. But since it is moving, its displacement varies with time. Hence, the constant velocity value is either positive or negative, depending upon the displacement is either increasing or decreasing. 

The displacement time graph illustrates both constant positive and constant negative velocity when an object moves forward and backward. 

Suppose a car moves forward on an inclined slope of a hill, and its motion is called constant positive energy. But if the driver cannot accelerate the car on an inclined plane, then the car starts moving backward, and its motion is termed as its constant negative velocity.

How is Constant Velocity Negative
How is Constant Velocity Negative

Read more about How Does an Inclined Plane Make Work Easier.

Draw a displacement time graph from the following data that includes displacement by the moving car on an inclined plane per unit time:

Displacement(meter)Time (secs)
00
201
402
603
804
1005
1006
907
808
709
6010
Displacement Time Graph
Displacement Time Graph

Also, calculate the constant positive velocity and constant negative velocity of the car.

Given:

For constant positive velocity-

s2: 80m

s1: 0s

t2: 4m

t1: 0s

For constant negative velocity:

s2: 60m

s1: 90m

t2: 10s

t1: 7s

Formula:

v→= s2-s1/t2-t1

Solution:

The constant positive velocity of car is calculated as,

v→= s2-s1/t2-t1

v→ = 80-0/4-0

v→ = 80/4

v→ = 20m/s

The car moves on an inclined plane with a constant positive velocity of 20m/s.

The constant negative velocity of car is calculated as,

v→ = s2-s1/t2-t1

v→ =90-60/10-7

v→ =30/3

v→ = 10m/s

The car moves on an inclined plane with a constant negative velocity of 10m/s.

Read more about Velocity on an Inclined Plane.

When is Constant Velocity Negative?

The constant velocity negative is when an object moves in the opposite direction. 

The positive and negative signs of velocity reveal the direction of an object’s motion. So whenever an object moves in the opposite direction, it drives with constant negative velocity. But this negative direction is defined by the coordinate system to specify the position. 

An object’s final displacement may be either zero, positive or negative, larger, smaller, or the same as initial displacement. Hence, its constant velocity also is zero, positive or negative, when no force is applied.

The displacement time graph shows different shapes of slopes for different values of negative velocities. That means the slope appears more down for the high value of constant negative velocity than the low value of negative velocity, which demonstrates which object is moving faster than the other.

Usually, we estimate the velocity as positive. In contrast, we do not express the velocity in a negative value. Hence, the constant negative velocity is expressed as the relative motion between two objects. One object’s forward direction is the opposite to the others when both move oppositely. The relative motion between two oppositely moving objects is specified by its coordinate system (x,y,z,t).

Suppose two athletes, A and B, run opposite each other with constant velocity. For athlete A, athlete B is running with constant negative velocity. Hence we say athlete B is running with a constant negative velocity with respect to athlete A. Whereas, for athlete B, athlete A is running with a constant negative velocity. So we can say it is a constant negative velocity of athlete A with respect to athlete B.

When is Constant Velocity Negative
When is Constant Velocity Negative

Read more about Relative Motion.

Constant Negative Velocity Example

The constant negative velocity example depicts the opposite motion of an object which is listed below:

Constant Negative Velocity Examples
Constant Negative Velocity Examples

Inclined Plane

When pushing the box upon an inclined slope-like ramp, it slides with constant positive velocity as it pushes it in a positive forward direction. Suppose we leave the box midway through the slope; it slides backward on an inclined ramp in a negative direction. So we can say it slides oppositely with constant negative velocity.

Automatic Door

It is another example where an object moves with constant velocity in a positive direction when we push it. But if we leave the door after we pass, it automatically starts to move in the opposite direction to being closed. While this opposite automatic motion, the door moves with constant negative velocity.

Steering Wheel

It is a constant negative velocity example in terms of rotational motion. While taking a left or right or U-turn, we rotate the steering wheel fully in a clockwise or anticlockwise direction. In such a case, steering wheels move with constant positive angular velocity. To turn the vehicle, we need to rotate the wheel in the opposite direction again, where it moves with constant negative angular velocity.

Dialing Old Telephone

An old-fashioned example depicts an object moving with constant angular motion. While dealing with the telephone, we rotate the dialer in the clockwise direction. Hence its constant angular velocity is positive.

But when we leave the dealer after one rotation, it automatically comes to its original position. The old telephone’s automatic opposite motion portrays that its constant angular velocity is negative.

Stretched Spring

When we stretch the spring forward, its displacement increases with time; hence it moves with constant positive velocity. But the spring has the restoring force that enables it to regain its original position after releasing the stretch. Hence, the spring again moves in the opposite direction to regain its original position due to spring force. Since it moves in the opposite direction, its constant velocity is negative.

Stretched Rubber

Like the last example, rubber also stretches with constant positive velocity in a positive direction. But the rubber material also has the restoring force, which allows it to regain its original position. Hence, after we remove the stretch on the rubber, it moves in the opposite direction regain due to elastic force. Therefore, its constant velocity is negative.

Moving Car

Suppose a boy is standing at the side of the road. If the car is moving away from the boy, then the car moves in a positive direction with the constant positive velocity with respect to the car itself and also with respect to the boy on the road.

But if the car moves toward the boy, then the car moves with constant positive velocity to itself only; but it moves with the constant negative velocity with respect to the boy.

Constant Negative Velocity Example
Constant Negative Velocity Example

Running Trains

When two trains run on separate railway tracks, their motion is relative. Therefore, one’s constant positive velocity appears as the constant negative velocity to another train and vice-versa.

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