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Important Formula of Time and Distance

(1) . Time taken by a train x meters long to pass a pole or standing man or a post= Time taken by the train to travel x meters.

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(2) . Time taken by a train x meters long to pass an object of length y meters= Time taken by the train to travel (x+y)metres.

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(3). If two trains are moving in opposite directions at v₁ m/s and v₂ m/s, then their relative
speed = (v₁ + v₂)m/s

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(4). Assume two trains of length x metres and metres are moving in opposite directions at v₁ m/s, and v₂m/s then the time taken by the trains to cross each other =

x+y/v₁ + v₂

seconds.

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(5). Assume two trains of length x metres and y metres are moving in the same direction at v₁m/s and v₂ m/s where v₁m/s > v₂m/s Then the time taken by the faster train to cross the slower train =

x+y/v₁ - v₂

seconds

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(6) . Relation between time, distance and speed: Speed is distance covered by a moving object in unit time.

Speed =

Distance Covered/Time Taken

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(7) . Relation between two values when third is constant.

(i) . When speed is constant distance covered by the object is directly proportional to the time taken.

If S_a=S_b,then

D_a/D_b

=

T_a/T_b

(ii) . When time is constant speed is directly proportional to the distance travelled.

If T_a=T_b , then

S_a/S_b

=

D_a/D_b

(iii) . When distance is constant speed is inversely proportional to the time taken ie if speed increases then time taken to cover the distance decreases.

If D_a=D_b then ,

S_a/S_b

=

T_a/T_b

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(8). If the speed of the body is chnaged in the ratio x:y, then the ratio of time taken changes in the ratio y:x.

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(9). Conversion
(a). xkm/hr = (x.

5/18

)m/s.

(b). xm/s = (x.

18/5

)km/hr.

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(10) . Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr. Then, the average speed during the whole journey is   (

2xy/x + y

)km/hr.

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(11) . If two persons A and B start at the same time in opposite directions from to points (say P and Q respectively) and after passing each other they complete the journey A and B hrs respectively , Then

Speed of A : Speed of B = √b : √a

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