[Physics Class Notes] on Relative Speed Pdf for Exam [2024]

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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