Shortcut 1 :
speed = distance/time
Shortcut 2 :
distance = speed ⋅ time
Shortcut 3 :
time = distance/speed
Shortcut 4 :
If the speed is given km per hour and we want to convert it in to meter per second, we have to multiply the given speed by 5/18.
Example :
90 km/hr = 90 ⋅ 5/18 = 25 meter/sec
Shortcut 5 :
If the speed is given meter per sec and we want to convert it in to km per hour, we have to multiply the given speed by 18/5.
Example :
25 meter/sec = 25 ⋅ 18/5 = 90 km/hr
Shortcut 6 :
Let the length of the train be L meters.
Distance traveled to pass a standing man = L meters
Distance traveled to pass a pole = L meters
Shortcut 7 :
Let the length of the train be 'a' meters and the length of the platform be 'b' meters.
Distance traveled to pass the platform is
= (a + b) meters
Shortcut 8 :
If two trains are moving on the same directions with speed of 'p' m/sec and 'q' m/sec (here p > q), then their relative speed is
= (p - q) m/sec
Shortcut 9 :
If two trains are moving opposite to each other in different tracks with speed of 'p' m/sec and 'q' m/sec, then their relative speed is
= (p + q) m/sec
Shortcut 10 :
Let 'a' and 'b' are the lengths of the two trains.
They are traveling on the same direction with the speed 'p' m/sec and 'q' m/sec (here p > q), then the time taken by the faster train to cross the slower train
= (a + b)/(p - q) seconds
Shortcut 11 :
Let 'a' and 'b' are the lengths of the two trains.
They are traveling opposite to each other in different tracks with the speed 'p' m/sec and 'q' m/sec, then the time taken by the trains to cross each other
= (a + b)/(p + q) seconds
Shortcut 12 :
Two trains leave at the same time from the stations P and Q and moving towards each other.
After crossing, they take 'p' hours and 'q' hours to reach Q and P respectively.
Then the ratio of the speeds of two trains is √q : √p.
Shortcut 13 :
Two trains are running in the same direction/opposite direction.
The person in the faster train observes that he crosses the slower train in 'm' seconds.
Then the distance covered in "m" seconds in the relative speed is
= length of the slower train
Shortcut 14 :
Two trains are running in the same direction/opposite direction.
The person in the slower train observes that the faster train crossed him 'm' seconds.
Then the distance covered in 'm' seconds in the relative speed is
= length of the faster train
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