Key concepts:
1. If two objects are moving in opposite directions towards each other at speeds $u$ and $v$, then
Relative speed = Speed of first + Speed of second = $u + v.$
2. If the two objects move in the same direction with speeds u and v, then
Relative speed = difference of their speeds = $u - v$.
Important Models:
Model 1. one Pole and one Train:
![one pole and one train](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg2o2vwoTfiQ5a3A1Ppdti2Rd7OutQyZCL5ODaBAP299ItsYRxtq48QeKCBb5GWDJuLNAPXibj6DB8ohWsDtNgxpBZZJMSYdCo-93BpSy_cFRGctIlGTdprxgyMabGAUTcxSVdHSo2lPyAy/s200/pole.png)
Length of The Train (m) = Speed of the Train (m/s) × Time taken to cross the pole (s)
Formula: $L = v \times t$
Model 2. one Train and one Bridge:
![one bridge and one train](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhmW0DBA-auwjwyUxuvCLokWSZwZlgddoAhP77lyi78JBDCmtIeQ721ogRNiot_Ys1J3hbf38lDOAuog-AFuvZvNkK_cS9QpQrrC7re2FTe30n6YOr5RRRtsdiZP7pwTogytmDbgBpGlwKc/s320/bridge.png)
Length of the Train + Length of the Bridge (m) = Speed of the Train (m/s) × Time taken to cross the bridge(s)
Formula: ${L_1} + {L_2} = v \times t$
Model 3. one Train with speed speed $u$ and one moving person with speed $v$
Case 1: If both are moving in same direction
![trains and man moving in same direction](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEir56XusBS73qQZwwvoe6W2UB6-W5mzJkp-MFeQG2gxM1-OGEL2jLtA3P1feHWGwxvJWcdKapu83a0VoDb6flRfBF8l-dSbFfkv6ignaQtHByzvW0l3FydmnMTt2Gl460F0lJQe8kABdlnp/s320/mm2.png)
Length of The Train (m) = [Speed of the Train - Speed of the Man] (m/s) × Time taken to cross the man (s)
Formula: $L = \left( {u - v} \right) \times t$
Case 2: If both are moving in opposite direction
![one train and one man opposite direction](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-M9ws9cbd9VQDU_xm62sBI0dkNWPo5BAUUoRG7qQ2IejMdzWUXFgaYXUf7zTYp6X0EDIHIBtWk5wD5NGaEESEi1RpL691lPT17CjCfBu4B1eDdEABBatjKlHXupIJmBncWvUF9ZVqoloP/s320/mm1.png)
Length of The Train (m) = (Speed of the Train + Speed of the Man) (m/s) × Time taken to cross the man (s)
Formula: $L = \left( {u + v} \right) \times t$
Model 4. 2 Trains with speeds $v$, $u$
Case 1: If both are moving in same direction
![two trains same direction](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJnlf_g_rTzIGPbCvb59-z4gh35a3qeI2PxQpJkTFaTkE29C9d4hMOZhyphenhyphen3ewsBtHIvkTKlgc17O05dkHAZ2bPmwoiwE-xAi-OrP-ZLrTZe4kvpO6KC7i-FvWM4oaf7Lce3Alz6_mPEfZrm/s320/2ts.png)
(Length of The Train 1 + Length of the Train 2)(m) = (Speed of the Train1 - Speed of the Train 2) (m/s) × Time taken to cross (s)
Formula: ${L_1} + {L_2} = \left( {u - v} \right) \times t$
Case 2: If both are moving in opposite direction
![two trains opposite direction](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhkvTCQPFIQELvu-fcPzlJcz1uGM_8HB0YmVvmJOBrVeAuVmu5B3GJEDc2ugeYuUlIpWnwf3WB8GfwGG_iCejE7RgMzkqF-8lQRr7ZBS8bKlJVO2fiTChvYrNRQdpoTPYQ1DA_Tij5VmdzO/s320/2to.png)
(Length of The Train 1 + Length of the Train 2)(m) = (Speed of the Train1 + Speed of the Train 2) (m/s) × Time taken to cross (s)
Formula: ${L_1} + {L_2} = \left( {u + v} \right) \times t$