Relative Speed - Meaning, Explanation, Formula, and Train-based Questions
The theory of Relative Speed is vital to most physicists. When do we consider the body to be in motion? If you are lying still on the ground, are you in motion, or are you at rest? The answer to the query is that if you change your relative position with respect to a frame of reference, then you are in motion; otherwise, you are in a state of rest.
If one moves towards you, we can calculate his/her speed by evaluating the difference between their relative spots taking a fixed point as a frame of reference with respect to you.
What is the Meaning of Speed?
Speed is known as distance traveled per unit of time. It is how fast an item is moving. Speed is the scalar quantity, which is the magnitude of the velocity vector. Speed doesn't have a direction. If an object is moving slower, then it is considered to be at a lower speed, whereas if an object is moving faster, then it is considered to be at a higher speed.
Explanation
The conventional method to calculate a constant velocity of an object moving in a straight line is mentioned in the below formula.
r = d / t
Where,
r is rate, or speed (sometimes denoted as v, for velocity)
d is the distance moved
t is the time taken to complete the motion
The average speed of an object over an interval of time is determined by the above equation. The object might be traveling faster or at a slower speed at different points during the time interval. Here the average speed is the total distance traveled by an object divided by the total time taken.
If one person initiates movement towards the other, the only way to know their speed is by measuring the position relative to the fixed position, which is most likely to be the other person. Here, both the cases need to be taken into account, whether they move or are still.
If they are moving in the same direction but at different speeds, then one person will appear to be moving slower than they are. For example, a person moves at a speed of 20m/s towards the east, and the second person moves at a speed of 22m/s east. Then the second person will appear to be moving away at 2m/s from the first person. If both people move towards each other, then they are moving faster than normal.
Types of problems in Relative Speed Calculation
Ratio Based Issues- There are certain ratio-based problems while calculating Relative speed like if both objects are moving with speed and in the same direction. Here one object is A and the other is B, so the ratio for speed and distance be A: B and to calculate the time to cover the same distance then the ratio be B: A, but the concept is valid only when the given distance, time or speed is constant.
Travel time and Meeting Time- Whenever two objects or persons start moving towards each other at the same speed and at the same time then the meeting point of both objects should be the same and the time taken should also be the same. The distance covered should be proportional to the speed.
Problems with Boats and Streams- The problem here is with the speed of the river which is the medium and the speed of the boat or swimmer which is in water which is also not constant. It depends on two conditions when the water is steady or there's movement in the water at the time current flows. In these conditions when the boat moves against the flowing current then it will move "upstream" and when the boat moves with the flowing current then it goes "downstream" here the speed defers in constant water and in moving water.
Do you Know?
With the help of the reference frame, we can only define time and space. There is no such thing as fixed points; hence we need to look at the frames. When we say something, we must know that it is always moving. So the frame of movement must be recognized to precisely describe speed.
Relative Speed Formula
Consider two bodies moving at a different speed in the same direction.
Let the speed of the first body be: x km/hr.
And the speed of the second body is y km/hr.
So, their relative speed is equal to (x – y) km/hr x>y
Then,
The time after which both bodies meet = distance traveled / relative speed
= dkm/ (x – y) km/hr
Now, we know that the relative speed is the speed of one object with respect to another.
So, if time after which both the body moves is given,
Suppose, time = t hrs.
Then, distance covered in‘t’ hours = relative speed * time
= (x – y) km/hr * t hrs.
Train Speed Formula
Here are a few problems on trains for quick solutions of train-based questions:
Remember some crucial formulas of train problems for quick solutions.
x km/hr = x*(5/18) m/s.
x m/s =x*(18/5) km/hr
Time taken by the train of length/meters to pass a pole or a single post or a standing man is equal to the time taken by the train to cover / meters.
Time taken by the train of length l meters to pass an unmoving object of length b meters is the time taken by train to cover (l + b) meters.
Suppose bodies or two trains are moving in the same direction at u m/s & v m/s, where u>v then the relative speed in the same direction = (u - v) m/s.
Suppose two bodies or two trains are moving in the opposite direction at u m/s and v m/s, then their relative's speed = (u + v) m/s.
Consider two trains of length A, B are moving in the opposite direction at u m/s & v m/s, then period taken by the trains to cross each other:
= (A+B)/(u+v)
Consider two trains of length A meters and B meters going in a similar direction at u m /s & v m/ s, then the time taken by the faster train to cross the slower train
= (A+B)/(u-v)
Consider two bodies (or trains) starting at similar time from points A and B in the direction of each other and after crossing they take a and b sec in reaching B and A respectively, then (A’s speed): (B's speed) =\[(\sqrt{b}: \sqrt{a})\].
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FAQs on Relative Speed
1. What is relative speed and why is it important in Physics?
Relative speed is the speed of an object with respect to another object, which may be stationary or in motion. It is a fundamental concept because all motion is relative; an object's speed can only be described in relation to a specific frame of reference. For example, a passenger walking inside a moving train has one speed relative to the train and a completely different speed relative to the ground.
2. How is relative speed calculated for objects moving in the same and opposite directions?
The calculation depends on the direction of motion:
- Same Direction: When two objects, A and B, move in the same direction with speeds VA and VB, their relative speed is the difference between their individual speeds: Vrelative = |VA - VB|.
- Opposite Directions: When two objects, A and B, move towards or away from each other, their relative speed is the sum of their individual speeds: Vrelative = VA + VB.
3. What is the difference between relative speed and relative velocity?
The key difference lies in their nature as scalar and vector quantities. Relative speed is a scalar quantity, meaning it only has magnitude (a numerical value). It tells you 'how fast' an object is moving relative to another. In contrast, relative velocity is a vector quantity, possessing both magnitude and direction. It describes 'how fast and in what direction' an object is moving relative to another. For example, two cars moving towards each other at 50 km/h each have a relative speed of 100 km/h, but their relative velocities would have opposite signs.
4. How does the concept of relative speed apply to solving problems involving trains?
Relative speed is crucial for solving classic train problems. When calculating the time taken for two trains to cross each other, the total distance to be covered is the sum of their lengths. This distance is then divided by their relative speed. For example:
- To find the time for a faster train to overtake a slower train moving in the same direction, you use the difference in their speeds (Vrelative = Vfast - Vslow).
- To find the time for two trains to pass each other while moving in opposite directions, you use the sum of their speeds (Vrelative = Vfast + Vslow).
5. Can two objects have zero relative speed even if they are moving? Explain with an example.
Yes, it is possible. Two objects have zero relative speed if they are moving with the exact same velocity (i.e., the same speed and in the same direction). In this scenario, the distance between them remains constant. For example, if two cars are travelling side-by-side in adjacent lanes on a highway, both at 90 km/h, their relative speed with respect to each other is zero. To a passenger in one car, the other car appears to be stationary.
6. Explain the concept of upstream and downstream motion in the context of relative speed.
Upstream and downstream are terms used to describe the motion of an object (like a boat or swimmer) in a moving medium (like a river). Their effective speed is a result of relative motion:
- Downstream: The object moves in the same direction as the current. The speed of the current adds to the object's speed, so the relative speed with respect to the riverbank is (Vobject + Vcurrent).
- Upstream: The object moves against the current. The speed of the current opposes the object's speed, so the relative speed with respect to the riverbank is (Vobject - Vcurrent).
7. Why is the 'frame of reference' a critical concept for understanding relative speed?
A frame of reference is the coordinate system or the set of axes within which we describe the position, orientation, and motion of an object. Motion is not absolute; it is always described relative to something else. Without defining a frame of reference, a statement about speed is incomplete. For instance, a person sitting on a bus is at rest relative to the bus (the frame of reference), but is moving at 60 km/h relative to the ground (a different frame of reference). Therefore, specifying the frame of reference is essential to avoid ambiguity and correctly apply the principles of relative motion.
