In the last section, we had learned some basics concepts related to time, speed & distance. We learned some formulas, fundamentals of average speed, and many more. In this section, we will discuss about** Relative Speed**.

Let’s take an example If a train passes a stationary object (bridge, platform, etc.) having some length, then the distance covered by train is equal to the sum of the lengths of the train and that particular stationary object which it is passing.

Too much theory huh? let’s take an example.

**E.g.** Let Carry was driving a car at a speed of 5 m/s whose length is 4 m. Find the time required by Carry’s car to cross the 6 m long shop?

So let’s begin

Total distance = length of Carry’s car + length of shop

⇒ 4 + 6 = 10m

Speed = 5 m/s

T = d/v

⇒ 10/5 = 2s (**Ans**.)

We took the case where only one body was in motion but what would happen when two bodies in motion. Let’s try to connect this with what we had studied in the previous unit.

By keeping this simple there would be two cases

**Both bodies are traveling in the same direction:**When both objects are traveling in the same direction then the speed would get**subtracted.**

E.g. Suppose two trains travel on the parallel platforms in the same direction and you are in one train, so relative speed would be (Speed of Ist – Speed of IInd).

**Both are traveling in different directions:**When both objects are traveling in the opposite direction then the speed would get**added**.

**E.g. **Suppose two trains travel on the parallel platforms in the opposite directions and you are in one train, so relative speed would be (Speed of Ist + Speed of IInd).

Yes, we all experienced this, Now let’s do some questions.

**E.g.** Two trains of lengths 80 m and 90 m are moving in opposite directions at 10 m/s and 7 m/s, respectively. Find the time taken by the trains to cross each other.

**STEP –**1 Our first step is to check whether all quantities are in the same unit. (e.g. if time is in hours speed should be in km/h or mile/h etc.)

Yes, units are the same.

**STEP-2 **Is train in the opposite direction or same?

Opposite.

**STEP-3** Find total distance and put in the formula.

Total distance = 80 + 90 =170 m

Relative speed = 10 + 7 = 17 m/s (addition because direction is opposite)

Time = distance/speed

⇒ 170/17 = 10 s (**Ans**.)

**E.g.** Two trains of lengths 90 m and 90 m are moving in the same directions at 10 m/s and 7 m/s, respectively. Find the time taken by the trains to cross each other.

Total distance = 90 + 90 = 180 m

Relative speed = 10 – 7 = 3 m/s (subtraction because both are in same direction)

time = distance/speed

⇒ 180/3 = 60 s (**Ans**.)

**E.g.** Two trains of lengths 75 m and 95 m are moving in the same direction at 9 m/s and 8 m/s, respectively. Find the time taken by the faster train to cross the slower train.

**APPROACH: **Close your eyes and assume two trains are moving in the same direction. The first face of the faster train will cross slow train completely then the slower train has been passed by a faster train.

Total distance travelled by faster train to cross the slower train = length of slower train + length of faster train

⇒ 75 + 95 = 170 m

Relative speed = 9 – 8 = 1 m/s

Time = 170/1 = 170 s (**Ans**.)

**E.g.** Train A of length 120 m can cross a platform of length 240m is in 18 seconds the ratio of speed train A and Train B is 4:5. The find the length of train B if train B can cross a pole in 12 seconds.

**APPROACH:** Do you also get annoyed by seeing so much data? Just relaxes and solve by reading line by line.

Length (A) = 120 m

A cross platform in 18 seconds

Total distance = 120 + 240 = 360 m

Time = 18 s

Speed(A) = 360/18 = 20 m/s

It is given that, ratio of speed of A : B = 4 : 5

Speed of B = 20 × 5/4 = 25 m/s

Train B passes a pole in 12 s

By formula,

Distance = speed × time

⇒ 25 × 12 = 300 m (**Ans**.)

**E.g.** A train passes a standing man in 6 s and a 210 m long platform in 16 s. Find the length and the speed of the train.

Let the speed of train be *v* and length of train be:

**Case – 1**

Train passes a man in 6 s

Speed = distance/time

*v *= *l*/6 ⇒ *l* = 6*v* (i)

**Case – 2**

Train passes a platform in 16 s

Speed = distance/time

*v *= (*l* + 210)/16

By using (i)

*v = *(6*v* + 210)/16

16*v =* 6*v* +210

⇒ 10*v =* 210

⇒ *v =* 21 m/s (**Ans**.)

And *l = *6*vi* ⇒ *l* = 6 × 21 = 126 m (**Ans**.)

1. Time and Distance Part 1 – https://www.rankershubindia.com/speed-distance-and-time-part-1/

2. Time and Distance Part 3 – https://www.rankershubindia.com/speed-distance-and-time-part-3/

3. Time and Distance Part 4 – https://www.rankershubindia.com/speed-time-and-distance-part-4/

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