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Realtive velocity, as the name suggest, is relative in nature. It is the velocity of an object with respect to another observer. Velocity of an object A relative to another object B is the velocity that A would appear to have by an observer moving with the B. Relative velocity is used in such occasions where one or more objects move in a frame which is non-stationary with respect to another observer. For example, an aeroplane encountering the wind during its flight. In all such cases, we calculate relative velocity so as to describe the object’s complete motion. Relative velocity is an important concept in physics as it allows us to understand how objects move and interact with one another by measuring the velocity of two objects in relation to each other.
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Key Terms: Velocity, Direction, Physics, Frame of Reference, Vector
What is Relative Velocity
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The relative velocity of an object is defined as velocity of an object in relative to or with respect to another observer. In simple terms it is the time rate of change of position of an object relative to another object. Relative velocity is also defined as the vector difference between the velocities of two bodies, i.e., the velocity of a body with respect to another body regarded as being at rest. It is the measure of how fast two objects are moving with respect to each other.
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Relative Velocity Formula
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The relative velociity is measured within an object as per the observer. It can be measured using an intermediate reference frame. The relative velocity formula is expressed as:
| VAB = VA + VB |
where,
VAB = relative velocity,
VA = velocity of object A and
VB = velocity of object B
The relative velocity is calculated differently for th eobjects moving in same direction and the objects moving in opposite directions.
- When objects are moving in same direction
here, the relative velocity will be:
VAB = VA – VB or VB – VA
As both the cars(objects) are moving in the same direction, their velocities will be subtracted.
- When objects are moving in the opposite direction
here, the relative velocity will be
VAB = VA + VB
As both the cars(objects) are moving in the opposite direction their velocities can be directly add up.
Also Read:
| Chapter Related Concepts | ||
|---|---|---|
| Angular Motion | Angular Displacement | Angular Velocity Formula |
| Types of Motion | Angular Acceleration | Angular Speed |
Solved Examples
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Relative velocity is a widely used concept in physics. To understand better a few examples are given below:
| Example: Bus A travel with a speed of 40 m/s towards North and bus B travel with a speed of 60 m/s towards South. What is the relative velocity? Solution: Speed of bus A= Va = 40 m/s (towards north) Speed of bus B= Vb = 60 m/s (towards south) As both the buses are moving in opposite direction, so relative velocity is: Vab = Va – (-Vb) = 40 – (-60) = 100 m/s Example: How long will a girl sitting near the window of a train travelling at 36 km h-1 see a train passing by in the opposite direction with a speed of 18 km/h? The length of the slow-moving train is 90 m. Solution: Velocity of train = Vt = 36 Km/h = 36 × 5/18 m/s = 10 m/s Velocity of passenger moving in opposite direction = Vp = 18 Km/h = 18 × 5/18 m/s = 5 m/s The relative velocity of the slow-moving train with respect to the girl is Vtp = Vt – (-Vp) = Vt + Vp Vtp = (10 + 5) m/s = 15 m/s. As the girl will watch the full length of the other train, to find the time taken to watch the full train: Using relative speed = distance / time 15 = 90/t t = 90/15 = 6 sec |
Things to Remember
- The relative velociity is measured within an object as per the observer.
- It is the time rate of change of position of an object relative to another object.
- Relative velocity is calculated by the formula: VAB = VA + VB
- It is the measure of how fast two objects are moving with respect to each other.
- Relative velocity is also defined as the vector difference between the velocities of two bodies.
Also Check Out: Derivation of the Equation of Motion
Sample Questions
Ques: Define relative velocity. (1 Mark)
Ans: The relative velocity of an object is defined as velocity of an object in relative to or with respect to another observer. In simple terms it is the time rate of change of position of an object relative to another object.
Ques: How is relative velocity different with velocity? (1 Mark)
Ans: Velocity is measured with respect to a reference point which is relative to a different point. While relative velocity is measured in a frame where an object is either at rest or moving with respect to the absolute frame.
Ques: A person in an enclosed train car, moving at a constant velocity, throws a ball straight up into the air in her reference frame. Where does it land if the car rounds a turn? (2 Marks)
Ans: The ball will land to the right of the point from which it was thrown if the car takes a left turn and vice versa.
Ques: What is the need of using relative velocity? (2 Marks)
Ans: The need for using relative velocity is that it is used for differentiating if the object is at rest or moving.
Ques: A motorcycle travelling on the highway at a velocity of 120 km/h passes a car travelling at a velocity of 90 km/h. From the point of view of a passenger on the car, what is the velocity of the motorcycle? (3 Marks)
Ans: Let us represent the velocity of the motorcycle as VA and the velocity of the car as VB.
Now, the velocity of the motorcycle relative to the point of view of a passenger is given as
VAB = VA – VB
Substituting the values in the above equation, we get
VAB = 120 km/h – 90 km/h = 30 km/h
Hence, the velocity of the motorcycle relative to the passenger of the car is 30 km/h.
Ques: If two cars A and B are moving with uniform velocities with respect to ground along parallel tracks and in the same direction. Let the velocities of A and B be 35 km/h due east and 40 km/h due east respectively. What is the relative velocity of car B with respect to A? (2 Marks)
Ans: The relative velocity of B with respect to A, VBA = VB – VA = 5 km/h due east
Ques: If two trains A and B are moving with uniform velocities along parallel tracks but in opposite directions. Let the velocity of train A be 40 km/h due east and that of train B be 40 km/h due west. Calculate the relative velocities of the trains. (3 Marks)
Ans: Relative velocity of A with respect to B, VAB= 80 km/h due east
Thus to a passenger in train B, the train A will appear to move east with a velocity of 80 km/h
The relative velocity of B with respect to A, VBA= 80 km/h due west
To a passenger in train A, the train B will appear to move westwards with a velocity of 80 km h−1
Ques: How long will a boy sitting near the window of a train travelling at 36 km h-1 see a train passing by in the opposite direction with a speed of 18 km h-1. The length of the slow-moving train is 90 m. (3 Marks)
Ans: The relative velocity of the slow-moving train with respect to the boy is:
V = (36 + 18) km/h = 54 km/h = 54 × 5/18 m/s = 15 m/s
Since the boy will watch the full length of the other train, to find the time taken to watch the full train:
15 = 90/t
t = 90/15 = 4
Thus, it will take 6s to the boy.
Ques: Consider two trains A and B moving along parallel tracks with the same velocity in the same direction. Let the velocity of each train be 50 km h-1 due east. Calculate the relative velocities of the trains. (2 Marks)
Ans: Relative Velocity of B with respect to A is
VBA = VB – VA
VBA = (50 – 50) km/h = 0 km/h
Similarly relative velocity of A with respect to B is also 0 km/h.
Hence, the train will appear at rest to each other.
Ques: A swimmer’s speed in the direction of flow of a river is 12 km /h. Against the direction of flow of the river the swimmer’s speed is 6 km/h. Calculate the swimmer’s speed in still water and the velocity of the river flow. (3 Marks)
Ans: Let Vs and Vr, represent the velocities of the swimmer and river respectively with respect to ground.
Now,
Vs + Vr = 12 km/h
Vs – Vr = 6 km/h
Adding both the equations:
2Vs = 12 + 6 = 18 km/h
Vs = 18/2 = 9 km/h
Now, Vr = 12 – Vs = 12 – 9 = 3 km/h
The swimmer’s speed in still water is 9 km/h and the velocity of river is 3 km/h.
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