7 Facts on Negative Relative Velocity: With Problems


In this article, the topic, “negative relative velocity” will be summarizing in a brief manner. If the sign of the velocity is negative then it denoted the speed will be in the direction of opposite.

The Negative Velocity can be explain as, a matter when is move towards the opposite direction of the axis. When a body move towards the axis it’s denoted as positive sign and represent as, positive relative velocity while when a body is not move towards the axis its denoted as negative sign and  represent as negative relative sign.

So, if a body is situated at any place and we can observe that the line of sight is positive, any other body or matter is moving opposite direction of the line of the sight then the second body carrying negative relative velocity.

In another example is, is a car is move towards a positive axis at that that time another car at a unchanged speed comes and caught the car eventually then we easily can say that the car is comes from the negative axis according to the second one. That’s mean this incident is also indicate negative relative velocity.

Relative velocity:-

Relative velocity is the magnitude velocity relation for a matter to other matter.

Expression for the Relative velocity:-

Suppose two substances A and B are move from one place to another place continuously with average velocities. For A substance velocity is
va and B substance velocity is vb in one dimension towards the x – axis in similar direction.

Now, If the two substances A and B position arex A(O)andzB(O) for the respective time t = 0. In that case the two substances A and B position will be xA(t) and zB(t).

The expression can be written as,

xA(t)=xA(O)+vA(t)…..eqn(1)

xB(t)=xB(O)+vB(t)…..eqn(2)

The expression for the displacement from the matter A to the matter B can be express as,

x_B_A(t) = x_B(t) – x_A(t) …..eqn (3)

x_B_A(t) = {x_B(O) – x_A(O)} + (v_B – v_A)t…..eqn (4)

From the…..eqn (4) we easily can understand that, from the substance A to substance B the velocity will be vB–vA just because of the displacement the substance A to substance B changes continuously by the quantity of  vB–vA per unit of time.

For this reason, the expression for, the velocity for the substance of B relative to substance A can be express as,

vAB = vB– vA

In the same way, the expression for, the velocity for the substance of A relative to substance B can be express as,

vAB = – (vAB)

The unit for the relative velocity is, meter per second. The dimension for the relative velocity is ML1T-1

Difference between relative velocity and velocity:-

The major difference in between the relative velocity and velocity is, velocity is measured favour to a concern point while relative velocity not measured favour to a concern point it measured in different point.

Absolute velocity is measured in a substance where the substance motionless or move from one place to another respect to the absolute substance while relative velocity is not measured in a substance where the substance motionless or move from one place to another respect to the absolute substance.

Can relative velocity be negative?

Yes, relative velocity can be negative. The relative velocity is the dissimilation between two different velocities categorically of their magnitude, so the value of relative velocity can be negative.

Negative relative velocity graph:

When the first object P has more velocity compare to the second object that time the second object has lesser velocity, object P will be easily able to cross object Q and hence, the difference between the distance of the second object with respect to first object will be negative.

negative relative velocity
Image – Negative relative velocity graph

What does it mean if relative velocity is negative?

The meaning of the negative relative velocity means when a matter’s movement is happened towards opposite direction of the axis.

How can relative velocity be negative?

A matter is move towards in the direction of negative in simple way we can say that the matter contains negative velocity. If a matter is slowing down then the acceleration of the vector is pointed at the direction of the opposite.

When relative velocity is negative?

Negative velocity means a substance is move in the direction of the opposite towards the axis. So, if any substance is situated at any place and we observe that the line of sight is positive, any other body or matter is moving opposite direction of the line of the sight then the second body carrying negative relative velocity.

Problem:-1

An aeroplane is moved from Kolkata to Mumbai at that time the speed is 480 kilometer per hour. When the aeroplane is travelled that time combustion gas is exit at the speed of 1500 kilometer per hour.

Determine the amount of speed of the later by means of respect to a watcher on the surface.

Solution:-

Assume that,

V1 represent the velocity for the combustion gases of the aeroplane.

Given data are,

The velocity of the aeroplane is,

Vp = 480 kilometer per hour

Relative velocity of the aeroplane’s combustion gas is,

Vgp= – 1500 kilometer per hour.

We know that,

Vgp = Vg – Vp

– 1500 = Vg – 480

Vg = -1500 + 480

Vg = – 1020 kilometer per hour.

An aeroplane is moved from Kolkata to Mumbai at that time the speed is 480 kilometre per hour. When the aeroplane is travelled that time combustion gas is exit at the speed of 1500 kilometre per hour.

The amount of speed of the later by means of respect to a watcher on the surface is – 1020 kilometer per hour.

Problem:-2

Two cars are move in a parallel direction road from north to south. Car A is moved in the direction of north. The speed for the car A is 70 kilometre per hour and car B is moved in the direction of south. The speed for the car B is 98 kilometre per hour.

Determine the negative relative velocity.

Solution:-

Given data are,

Velocity for the car A,

VA=70kilometre per hour

VA=70×10003600

VA=18.88 m/s

Velocity for the car B,

VB=–98 kilometre per hour

VB=–98×10003600

VB=–27.22metre per second

Two cars are move in a parallel direction road from north to south. Car A is moved in the direction of north. The speed for the car A is 70 kilometre per hour and car B is moved in the direction of south. The speed for the car B is 98 kilometre per hour.

The negative relative velocity is – 27.22 metre per second.

Problem:-3

A named boy driving his car at a speed of 60 meter per second and Y named boy driving his car at a speed of 20 meter per second and both boys direction will be same. Then prove that, the relative speed boy the Y named boy with respect to A named boy will be negative.

Solution:-

Y named boy speed with respect to A named boy = (Speed of B named boy) – (Speed of A named boy)

=> Y named boy speed with respect to A named boy = 20 meter per second – 60 meter per second

=> Y named boy speed with respect to A named boy = – 40 meter per second.

A named boy driving his car at a speed of 60 meter per second and Y named boy driving his car at a speed of 20 meter per second and both boys direction will be same. So, the relative speed boy the Y named boy with respect to A named boy will be negative (Proved).

Conclusion:

Relative velocity comes with a direction, it indicates a speed at a direction. If relative velocity becomes negative, it is that speed in the opposite direction.

Indrani Banerjee

Hi..I am Indrani Banerjee. I completed my bachelor's degree in mechanical engineering. I am an enthusiastic person and I am a person who is positive about every aspect of life. I like to read Books and listen to music. Let's connect through LinkedIn-https://www.linkedin.com/in/indrani-banerjee-2487b4214

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