Tuesday, 22 November 2016

Speed , Time and Distance

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Speed, Time and Distance (Quantitative Aptitude) for Bank PO, Clerk, SSC CHSL, CGL and other competitive exams Speed,time,distance,unit,conversion of units, relative speed,trains and boat and streams.

Speed 

• The rate at which any moving body covers a particular distance is called its speed .

• Speed = Distance / Time.

Time 

• It is the time duration over which the movement has occured. The unit used for measuring time is synchronous with denominator of the unit used for measuring speed.Thus,if the speed is measured in terms of km/h then time is measured in hours.

• Time = Distance / Speed.

Unit 

• SI unit of speed is metre per second (mps). It is also measured in kilometers per hour (kmph) or miles per hour (mph).

Conversion of unit

• 1 hour = 60 minutes = 60 × 60 seconds.
• 1 km = 1000 m 
• 1 km = 0.625 mile
• 1 mile = 1.60 km,i.e. 8 km = 5 miles
• 1 yard = 3 feet
• 1 foot = 12 inches
• 1 km/h = 5/18 m / sec
• 1 m/sec = 18/5 km/h
• 1 miles/hr = 22/15 ft/sec.

Average Speed

• Average speed = Total Distance / Total time.

• While travelling a certain distance d , if a man changes his speed in the ratio m:n,then the ratio of time taken becomes n:m.

• If a certain distance (d) ,say from A to B , is covered at 'a' km/h and the same distance is covered again say from B to A in 'b' km/h , then the average speed during the whole journey is given by:

• Average speed = (2ab/a + b) km / h

• Also , if t1 and t2 is time taken to travel from a and b A, respectively, the distance 'd' from A to B is given by :

d = (t1 + t2)  (ab / a+b)
d = (t1 + t2) (ab / b - a)
d = (a-b) (t1 t2t2 - t1)

• If a body travels a distance 'd' from A to B with speed 'a' in time tand travels back from B to A i.e. the same distance with m / n of the usual speed 'a' , then the change in time taken to cover the same distance is given by :

Change in time = ( m / n - 1) × t1 : for n > m
                             = ( 1 - n / m) × t1 : for m > n

• If first part of the distance is covered at the ratio of vin time t1 and the second part of the distance is covered at the rate of vin time  t2 , then the average speed is ( v1t1 +  v2t2 / t1 + t2).

Relative Speed

• When two bodies are moving in same direction with speeds s1 and s2 respectively,their relative speed is the difference of their speeds.

• Relative Speed = s1 - s2

• When two bodies are moving in opposite direction with speeds  s1 and s2 respectively,their relative speed is the relative speed is the sum of their speeds.

• Relative Speed = s1 + s2

Formula for vehicles and train

• If two persons (or vehicles or trains)start at the same time in opposite directions from two points  A and B , and after crossing each other they take x and y hours respectively to complete the journey,then

• Speed of first / speed of second =√y/x

Trains 

• A train is said to have crossed an object (stationary or moving ) only when the last coach of the train crosses the said object completely. It implies that the total length of the train has crossed the total length of the object.

• Time taken by a train to cross a pole / a standing man.

• Length of train / speed of train

• Time taken by a train to cross platform and bridge .

= length of train + length of platform  and bridge etc / speed of train 

• When two train with lengths L1 and L2  and with speeds S1 and Srespectively , then

(a) When they are moving in the same direction,time taken by the faster train to cross the slower train

=  L1+ L2 / difference of their speeds

(b) When they are moving in the opposite direction,time taken by the trains to cross each other

=  L1+ L2 / sum of their speed

• Suppose two train or two bodies are moving in the same direction at u km / h respectively such that  u > v , then
their relative speed = ( u - v) km / hr.

If their lengths be x km and y km respectively , then time taken by the faster train to cross the slower train (moving in the same direction) = (x+y/u-v) hrs.

• Suppose two trains or two bodies are moving in opposite directions at u km / h , then their relative speed = (u+v) km / h .

If their lengths be x km and y km , then :

time taken to cross each other = (x+y / u+v) hrs.

If a man is running at a speed of u m / sec in the same direction in which a train of length L meters is running at a speed v m / sec , then (v-u)m /sec is called the speed of the train relative to man.Then the time taken by the train to cross the man = 1/v-u seconds

• If a man is running at a speed of u m / sec in a direction opposite to that in which a train of length L meters is running with a speed v m / sec,then (u+v) is called  the speed of the train relative to man.

Then the time taken by the train to cross the man.
= 1/v-u seconds

• It two trains start at the same time from two points A and B towards each other and after crossing , they take a and b hours in reaching B and A respectively. Then,

A 's speed : B's speed = ( √b: √a).

Boat and Stream

Stream  It implies that the water in the river is moving or flowing .

Upstream → Going with the flow of the river.

Downstream → Going with flow of the river.

Still water → It implies that the speed of water is zero .

• Speed of boat with the stream (or downstream or D/S) (x+y) m /sec.

• Speed of boat against the stream (or upstream or U/S)(x-y) m/sec.

• Speed of boat in still water is x = (x+y)+(x-y)/2 = Downstream + Upstream / 2.

• Speed of the stream or current is Y = (x+y) - (x-y) / 2 =  Downstream + Upstream / 2.

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