7 Facts On Relative Velocity In Same Direction: With Problems

The relative velocity of objects in the same direction is described as if the two objects are traveling in the same direction. The immensity of the relative velocity of one object concerning another is identical to dissimilarities in the immensity of two velocities.

Relative motion is the motion correlated to some coordinate system, in addition to the ground. When the motion is described concerning the ground, the coordinate system becomes the ground. Suppose if the two objects are traveling in the same direction, the relative velocity reduces for both the objects then the relative velocity becomes zero.

The direction of relative velocity

Relative velocity has two directions and there are the same direction and opposite direction. But the relative velocity relies on the spectator who calculates it. Hence, the relative velocity of a gadget calculated by a definite spectator would be the relative velocity concerning them. Another spectator can attain a distant value for the velocity, even when the arrangement is with the same object.

relative velocity in same direction
Two birds moving in the same direction image credit: pixabay

The relative motion velocity mentions to the gadget, which is relative to a distinct gadget that could be immobilized, traveling with the same velocity, traveling deliberately, traveling with greater velocity, or traveling in the same or reverse direction.

When the two gadgets travel in the same direction and with the same velocity, then the relative velocity of both the gadgets becomes a minimum that is zero; suppose if the two gadgets are traveling in the opposite direction, then the relative velocity of the object concerning the other object would be maximum.

How to find the direction of relative velocity?

Relative velocity is generally the dissimilarities between two velocities. i.e., relative velocity = V1-V2; let us say if we have the variable VBA means we are considering the velocity of the object B about the object A, so, B is the object that we are considering that is the object in focus A is the frame of reference we have to find this by using the difference between the velocity of the object A and object B.

i.e., VBA= VA-VB where VB is truly the velocity of B concerning the earth.

Let us say if a train travels 30 miles per hour concerning the earth. Suppose if we were standing on the floor and did not move to you, the train would be moving at 30 miles per hour. If we write one subscript, VB, then assume that it’s always concerning something that is immobilized. In this case, a good example is an earth VA is the velocity of object A about the earth.

relative velocity in same direction
Train moving with respect to the earth image credit: pixabay

Now let us say if we want to define VCA, that is the velocity of C concerning A, so we can calculate it by subtracting VC and v A, i.e., VCA=VC-VA, now if we want to find VAC, that is

the velocity of object A about the velocity of object C where c is the frame of reference then VAC=VA-VC, similarly for VCB, VCB=VC-VB, and VBC, VBC=VB-VC.

So generally, the relative velocity is just the dissimilarities between the velocity of the object minus the velocity of the frame of reference

i.e., RV=Vobject-Vfr, so this is the formula for finding the direction of relative velocity

What is the relative velocity in the same direction?

Relative velocity is defined as “the two bodies are traveling in the same direction, the enormity of relative velocity of one body regarding another is equal to the change in the enormity of two velocities, and their discrepancy calculates the relative velocity”.

An example of relative velocity in the same direction is, considering the two cars which are moving in the same direction, one at 45 meters per second and the other 55meter per second. The relative velocity of two cars is 10 meters per second according to the vector addition. However, the enormity should remain the same but the velocity changes because of a change in direction.

relative velocity  in same direction
Two cars travelling in same direction image credit: pixabay

Consider the two vehicles are traveling with the velocity V1 and V2, respectively, in the same direction. The relative velocity of one vehicle concerning the other is equal to V1-V2. The V1 is subtracted with V2 because Subtracting the velocities is the only way for us to acquire the relative speed.

Relative velocity in the same direction formula

The formula to find the relative velocity in the same direction is

VAB = VA-VB

Let us consider two gadgets, A and B, which travel relative to one another. Then the relative velocity would be the velocity at which a gadget A will emanate to body B and vice versa. We can say that the relative velocity is the vector difference between the two gadgets.

The relative velocity of A about B = velocity of the gadget A – velocity of the gadget B.

Mathematically,

VAB= VA-VB

Where:

VA is the velocity of gadget A, and VB is the velocity of gadget B.

Suppose if the two metros travel in the same direction at u m/s and v m/s, where u is greater than v, then the relative velocity in the same direction = (u-v) m/s.

How to find relative velocity in the same direction?

If the two bodies travel in the same direction, then the relative velocity is the total value of the dissimilarities between the two velocities. Let us say body A is traveling quicker than body B. The immensity of the relative velocity V(r) = V(a)-V(b).

For example, consider the two buses traveling in the dual carriageways on the same road, and one is moving at 75mph, the other at 55mph, then the velocity is (75-55)mph = 20mph in the direction of the road. Each regulates that the relative velocity of the other has the identical immensity but reverse sign. Suppose if both travel at the same speed, then the relative velocity is zero, and the two buses remain at the same interval.

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Two buses travelling on the same road in a same direction image credit: pixabay

According to the theory of relativity; if the two bodies A and B are moving in the same direction, the relativistic formula to find out the relative velocity in the same direction is given by,

The formula gives the relative speed:

When the velocities of A and B are comparatively smaller than the velocity of light, then the above equation generally becomes

This equation is used to determine the relative velocity direction of the objects.

What is the relative velocity of objects with equal velocity?

The relative velocity of objects with equal velocity is defined as “the two objects traveling in the same direction with the equal velocity, their relative velocity is going to be zero. This illustrates that another may emanate to be at rest for one object” if two objects have the same velocity then, VQP=V2-V1.

Consider the two vehicles, A and B, are moving in the same direction with equal velocity; the inclination between the two-vehicle vehicles is 0 degrees. That is VA=VB.

As a consequence, the velocity of the vehicle A analogous to vehicle B is:

VAB =VA-VB=0

Correspondingly, the velocity of vehicle B analogous to vehicle A is:

VBA = VB-VA =0

Draw a position-time graph of two vehicles, A and B traveling through a straight line when their relative velocity is zero. (a): relative velocity is zero when two vehicles travel in the reverse direction to one another with the same velocity. A vehicle’s relative velocity does not rely on the supervision of motion.

Position time graph

Problems with relative velocity in the same direction

(1). A police van traveling on the main road with a speed of 50 km/hr sniping a bullet at the robber’s car, speeding away in the same direction with a speed of 195 km/hr. If the brawn speed of the bullet is 170 m/s, what speed does the bullet bash the robber’s car?

Solution,

Given the speed of the police van, VP=50km/hr

= 50×1000/3600 = 13.88 m/s

Speed of the robber’s car, Vr =195 km/hr

= 195×1000/3600= 54.166 m/s

Brawn speed of the bullet, 170 m/s

The bullet will contribute to the speed of the car, hence the speed of the bullet,

Vb= speed of the police van + brawn speed of the bullet

=13.88+170

=183.88 m/s

The relative velocity of the bullet about the robber’s car,

Vbr=Vb-Vr

=183.88 – 54.166 =129.714 m/s

i.e., the bullet will bash the robber’s car at 129.714 m/s.

(2). If the two cars A and B travel with constant velocities concerning the floor through collateral lanes and in the same direction. Let the velocities of car A be 45 km/hr due east and B is 50 km/hr due east, respectively. What is the relative velocity of car B about car A?

Solution,

The relative velocity of B with regard to A,

= 50-45 = 5 km/hr due east

Correspondingly, the relative velocity of A with regard to B,

That is,

45-50 = 5 km/hr due west

Conclusion

By reading all the facts mentioned above, we finally get to the conclusion that if two gadgets or bodies travel in the same direction through a straight line, the relative velocity of gadget A concerning the gadget B would be equal to the dissimilarities between the two velocities then the relative velocity in the same direction would be zero.

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