How To Calculate Negative Velocity: Example And Problems


In this article, we are going to discuss how to calculate negative velocity along with some problems and examples.

The velocity of the object is negative if the initial displacement of the object for time ‘t’ is greater than the preceding distance travelled by the object. It can also be found out by knowing the acceleration of the object during that time.

What is a Negative Velocity?

The velocity of an object is said to be a negative is the displacement of an object is in a direction opposite to its direction of acceleration.

It can be calculated by finding the difference between the initial and final position of an object divided by the time taken by the object for its displacement, given by the relation

v=(dx/dt)=(x2-x1)/(t2-t1)

If the initial position of the object with respect to the origin of the object was greater than the position at which it is displaced then the velocity of the object is negative.

How to calculate the negative velocity of the object?

The velocity of the object is negative if the speed of the object decreases with displacement, if it slows down, if an object is falling from the heights, etc.

Time taken to cover a distance should be noted, and the velocity of the object for a specific time duration can be calculated by finding the difference between the positions divided by the time taken for a change in position.

If the time taken to elapse the same distance takes longer and longer time then the velocity of the object is negative.

Problem 1: Consider an object accelerating down the ground from a certain height above the ground. It was noted that initially, the object was at a height of 1000 meters above the ground. After 1 minute the height of the object was found to be 760 meters. Find the velocity of the object.

Solution: We havex1=1000m, x2=760m, time taken t=1 min=60 seconds

Hence, velocity of the object is

v=(x2-x1)/(t2-t1)=(760-1000)/(60-0)=-240/60=-4m/s

Since the object is accelerating down, the displacement is negative.

How to calculate negative velocity from the position-time graph?

The position of the object at a certain time interval is noted and plotted on the graph and hence called position-time graph.

Since the velocity is a ratio of displacement v/s time, the slope of the position-time graph will give us the velocity of the object. If the object is accelerating down then we will have negative displacement with time.

Look at the following graph of displacement of an object jotted at different time duration.

how to calculate negative velocity
Position-Time Graph

From the graph, it is seen that the displacement of an object decreases with time. Consider two points on the slope of the graph (X1, t1) and (X2, t2). The slope of the graph is equal to the ratio of the difference between the points on the y-axis to the variation on the x-axis, hence the slope of the position-time graph will give us the velocity of the object.

Since the displacement is back-paddling with time, or the rate of change of position of an object slowing down lowers constantly then the velocity of the object is found to be negative. Well, the time is not reversible and only the position of the object matters for negative velocity.

Read more on acceleration.

How to calculate negative velocity from the negative acceleration and time graph?

The object is said to be accelerating if its velocity frequently changes with time.

Hence, the acceleration is the ratio of change in velocity of the object by the time required for a change to occur. The rate of change of velocity can be calculated by multiplying acceleration and time between which the acceleration is modified.

Since the acceleration is negative, this encapsulates that the velocity of the object is also negative. This is in the case when the object is decelerating in the opposite direction of motion.

Problem 2:Consider the following graph plotted for an acceleration of the object measured at different time duration.

how to calculate negative velocity
Negative Acceleration-Time Graph

Based on the above graph, calculate the velocity of the object when time t=6 seconds. Also, calculate the change in the velocity of the object in between t1=6 sec and t2=8sec.

Solution: The acceleration of the object at t= 6 sec is -30 m/s2. Since acceleration is related to the velocity by the equation

a=v/t

v=at

v=-30m/s2*6s=-180m/s

Hence, as per the graph the velocity of the object at time t= 6sec, the object was moving with the velocity of -180m/s. Since the acceleration is negative, this implies that the velocity of the object is also negative.

At time t=8 sec, the acceleration of the object seen in the graph is -40 m/s2. Hence the velocity at this point is

a=-40m/s2*8s=-320m/s

Therefore the change in the velocity of the object from t1=6 sec and t2=8sec is

Δv=v2-v1

Δv=-320-(-180)

Δv=-140m/s2

 

Hence, this implies that the velocity of the object has been reduced to -140m/s2 within 2 seconds.

Read more on Negative Velocity And Negative Acceleration: Why, How, Graph, Example And Detailed Facts.

Frequently Asked Questions

How to calculate displacement from the negative-velocity time graph?

The displacement is the product of the velocity of the object during that time.

Since the displacement of the object is in the reverse direction, the change in the position of the object is negative and hence the displacement is negative.

Why does the negative velocity exist?

If the displacement of the object is away from the direction of its motion then the change in position with respect to the origin is negative.

As the displacement of the body is found negative, the velocity of the object will also be negative as the change in time is always positive as it is irreversible whereas the position and direction of motion can be reversed.

Does the temperature affect the negative velocity of the particle?

The system gains internal energy when the temperature of the system rises.

The rise in temperature sets the particle in an agile motion and hence the velocity and therefore the acceleration of the particle increase.

What do you mean by the negative relative velocity?

The motion of the object relative to the other object is calculated as the relative velocity.

If the velocity of both the objects are in the same direction and the velocity of one object is more compared to the other then the object with less velocity has negative relative velocity in comparison to the other object into motion.

How can be the negative velocity constant?

The velocity is measured to be negative if the displacement of the object is in the opposite direction.

The negative velocity can be constant if the rate of change of position in the reverse direction of the motion of an object with respect to time remains the same.

How will you find out acceleration from the negative velocity time graph?

The acceleration is a change in the velocity of the object with time. Hence, acceleration will be equal to the slope of the graph of velocity and time.

The negative velocity indicates that the displacement of the object is in the reverse direction and if the velocity is decreasing with time then the acceleration of the object will also be negative.

AKSHITA MAPARI

Hi, I’m Akshita Mapari. I have done M.Sc. in Physics. I have worked on projects like Numerical modeling of winds and waves during cyclone, Physics of toys and mechanized thrill machines in amusement park based on Classical Mechanics. I have pursued a course on Arduino and have accomplished some mini projects on Arduino UNO. I always like to explore new zones in the field of science. I personally believe that learning is more enthusiastic when learnt with creativity. Apart from this, I like to read, travel, strumming on guitar, identifying rocks and strata, photography and playing chess. Connect me on LinkedIn - linkedin.com/in/akshita-mapari-b38a68122

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