Relative Speed in Opposite Direction Formula and Solved Examples
Do you know the meaning of relative speed? A moving body's relative speed is its speed in relation to another. It is possible to shorten the word "Relative" to "in comparison with". Two bodies' differences are used to determine their relative speeds while they are travelling in the same direction. However, when two bodies are travelling in opposition to one another, the relative speed is calculated by adding the speeds of the two bodies.
How to Calculate Relative Speed?
Keep in mind that the two bodies that are moving at different speeds but in the same general direction.
Assume the first body's speed be x km/hr and the second body's speed be y km/hr.
The relative speed will be $\left( {x - y} \right)$ km/hr
The moment both bodies eventually meet $= \dfrac{{{\rm{Travel \,distance}}}}{{{\rm{Relative\, speed}}}} = \dfrac{{d\,{\rm{ km}}}}{{\left( {x - y} \right){\rm{ km/hr}}}}$
Knowing that relative speed is the speed of one object in relation to another object.
Therefore, once the time for the meeting of both bodies is given,
Suppose time = t hrs
Then distance covered in t hours $= {\rm{Relative \,speed}} \times {\rm{Time}} = \left( {x - y} \right){\rm{ km/hr}} \times t{\rm{ hrs}}$
Relative Speed in the Same and Opposite Direction
Formula for Relative Speed:
The formula below demonstrates how to determine a moving object's constant velocity using the conventional approach.
$r = \dfrac{d}{t}$
Where, r is rate of speed, d is distance travelled and t is time.
The above equation determines the average speed of an object over time. The object may move more quickly or more slowly at certain points over the time period. The average speed of an object is equal to the total distance travelled divided by the total time travelled.
The difference in the speeds of two bodies moving in the same direction can be used to calculate their relative speed. It can be described as ${V_1} - {V_2}$.
The total of the speeds of two bodies can be used to calculate their relative speed when they are going in the opposite direction at different speeds. It can be described as ${V_1} + {V_2}$.
Examples on Concept of A and B Start from a Point in Opposite Direction
Example 1: A telegraph post is crossed by two trains of identical length in 10 and 15 seconds, respectively. Assuming that each train is 120 metres long. When will they cross each other in opposing directions, in seconds?
Solution:
Speed of first train = $\dfrac{{120}}{{10}} = 10m/s$
Speed of second train = $\dfrac{{120}}{{15}} = 8m/s$
Therefore, their relative speed $ = 12 + 8 = 20m/s$
Therefore, required time $\begin{array}{l} = \dfrac{{120 + 120}}{{20}} = 12\sec \end{array}$
Hence, the two trains cross each other in 12 seconds.
Example 2: A man is walking at a speed of 5 km/hr in the opposite direction from a train that is moving at 45 km/hr. What is the length of the train if it passes the man in 18 seconds?
Solution:
The man is approaching the speeding train from the opposite direction, thus:
$\text{Relative speed of train} = \left( {45 + 5} \right)km/hr\\ \Rightarrow \text{Relative speed of train} = \left( {50 \times \dfrac{5}{{18}}} \right)m/s\\ \therefore \text{Relative speed of train} = \dfrac{{250}}{{18}}\,m/s$
$\Rightarrow \text{Length of train} = {\rm{Relative \,speed}} \times {\rm{Time \,taken}}\\ \Rightarrow \text{Length of train}{\rm{ = }}\dfrac{{250}}{{18}} \times 18\\ \therefore \text{Length of train}= 250\,m$
Hence, the length of the train is 250 m.
Example 3: Running from the same location with speeds of 10 km/h and 5 km/h respectively are two athletes. If they move in the opposite direction, how far apart are they after 20 minutes?
Solution:
Speed of 1st athlete = 10 km/hr
Speed of 2nd athlete = 5 km/hr
Relative speed $ = \left( {10 + 5} \right)km/hr$
Time taken $ = 20\min = \dfrac{{20}}{{60}} = \dfrac{1}{3}$
$\text{Distance} = {\rm{Relative \,speed}} \times {\rm{Time \,taken}}\\ \Rightarrow \text{Distance}{\rm{ = 15km/hr}} \times \dfrac{1}{3}hr\\ \therefore \text{Distance} = 5\,km$
Hence, the two athletes are 5 km apart after 20 minutes.
Conclusion
This article helped us to learn the basic concept of relative speed. The basic definition of relative speed is explained. A brief idea about the topic is achieved. Also, some examples are studied which can help in solving real-life problems. The formula for relative speed is known and can be used to solve the questions related to relative speed. The topic of relative speed is important for learning as many day to day life problems can be solved using the understanding of this topic.
FAQs on Relative Speed in Opposite Direction Explained Clearly
1. What is relative speed in opposite direction?
Relative speed in opposite direction is the sum of the speeds of two objects moving towards each other. When two bodies move in opposite directions, their speeds add up because the distance between them decreases faster.
- Formula: Relative Speed = Speed₁ + Speed₂
- This concept is commonly used in time and distance problems.
- It helps calculate meeting time or distance covered before meeting.
2. What is the formula for relative speed when two objects move in opposite directions?
The formula for relative speed in opposite direction is Relative Speed = v₁ + v₂. Here, v₁ and v₂ are the speeds of the two objects.
- If one object moves at 40 km/h and the other at 60 km/h,
- Relative Speed = 40 + 60 = 100 km/h.
- This formula applies when they are moving directly towards each other.
3. How do you calculate time when two objects move towards each other?
Time taken to meet is calculated using Time = Distance ÷ (Sum of speeds). When two objects move in opposite directions, use relative speed.
- Step 1: Add both speeds.
- Step 2: Divide the total distance by the relative speed.
- Example: Distance = 200 km, speeds = 50 km/h and 50 km/h.
- Relative Speed = 100 km/h
- Time = 200 ÷ 100 = 2 hours.
4. Can you give an example of relative speed in opposite direction?
Yes, relative speed in opposite direction means adding the two speeds to find how fast they approach each other.
- A train moves at 80 km/h.
- A car moves towards it at 70 km/h.
- Relative Speed = 80 + 70 = 150 km/h.
- This means the distance between them decreases at 150 km per hour.
5. Why do we add speeds in opposite direction?
We add speeds in opposite direction because the distance between the objects decreases by both speeds combined. If one object covers 40 km in one hour and the other covers 60 km towards it, together they reduce the gap by 100 km in one hour.
- Opposite direction → speeds add.
- Same direction → speeds subtract.
- This is based on the concept of relative motion.
6. What is the difference between relative speed in same and opposite direction?
The key difference is that speeds are added in opposite direction and subtracted in same direction.
- Opposite Direction: Relative Speed = v₁ + v₂
- Same Direction: Relative Speed = |v₁ − v₂|
- Example: 60 km/h and 40 km/h
- Opposite → 100 km/h
- Same → 20 km/h
7. How do you find the meeting point of two objects moving in opposite directions?
The meeting point is found by first calculating the time to meet and then multiplying by either object's speed.
- Step 1: Time = Distance ÷ (v₁ + v₂)
- Step 2: Meeting distance from first object = Speed₁ × Time
- Example: Distance = 180 km, speeds = 60 km/h and 30 km/h
- Time = 180 ÷ 90 = 2 hours
- Meeting point from first object = 60 × 2 = 120 km.
8. What happens to relative speed if one object is stationary?
If one object is stationary, the relative speed equals the speed of the moving object. Since the stationary object's speed is 0,
- Relative Speed = v + 0 = v.
- Example: A car moves at 70 km/h toward a stationary pole.
- Relative Speed = 70 km/h.
- This is a special case of opposite direction motion.
9. How is relative speed used in train problems moving in opposite directions?
In train problems moving in opposite directions, relative speed is the sum of both train speeds.
- If two trains move at 90 km/h and 110 km/h,
- Relative Speed = 200 km/h.
- Time to cross each other = Total length ÷ Relative Speed.
- This method is widely used in aptitude and competitive exams.
10. What are common mistakes in relative speed in opposite direction problems?
A common mistake is subtracting speeds instead of adding them in opposite direction motion.
- Always remember: Opposite direction → Add speeds.
- Ensure units are the same (km/h or m/s).
- Convert units properly before applying formulas.
- Check whether the problem states same or opposite direction.
