TIME AND DISTANCE

  Hi readers today we discussing the chapter time and distance.
     in the concept of time, distance and speed is related to a particular object in motion.

Relation between Time, Distance and speed
   Speed is the distance covered by an object in one unit of time. It is calculated by dividing the distance traveled by the time taken.

Speed = Distance
                 Distance = Speed X Time
                 Time      = Distance

Important points for time and distance
·         If speed is constant, then distance covered by an object is proportional to time (more time, more distance).

·         If Time is constant, then distance covered by an object is proportional to its speed (More spped, more distance).

·         If distance is constant, then speed is inversely proportional to time. Therefore, 

·          a km\h = (aX5/18) m/s.

·          a m/s   = (aX18/5) km/h

·         If two objective are in motion and their speeds are a and b, respectively, then
(a)        Relative speed = a+b (if two objects are in opposite direction)
(b)        Relative speed = a-b  (if two objects are in same direction)
If the ratio of speeds of A and B is x:y, then the ratio oftime taken by them to cover the same distance is given by
            1/x : 1/y, i.e., y: x

 Convert 90 km/h into m/s.
We know that a km/h = (ax5/18) m/s
                   90 km/s = (90x5/18)m/s
                     5x5 = 25 m/s.

Example: A train covers 135 km in 5 hh, find the speed of the train.
Answer: we know that
                   Speed = Distance / time.
                   Speed = 135/5 = 27 km/h.

Example : a bike crosses a bridge with a speed of 108 km/h . what will be the length of the bridge if the bike taken 8 min to cross the bridge?
Answer: here, the length of thew bridge
                                                = distance travelled by bike in 8 min
                                                   = speed X time
    Given that speed is 108 km/h = 108X 5/18 m/s = 30 m\s
                    Time = 8 min = 8x 60 = 480 s
        Lenth of bridge = 480X 30 = 14400 m.

      Technique 1:
            When a cetain distance is covered at a speed A and the same distance is covered at a speed B, then the average speed during the whole journey is given by               
= 2 AB /A+B

 Example: mahesh covers a certain distance by car driving at 35 km/h and he returns back to the starting point riding on a bike with a speed of 25 km/h. find the average speed of the whole journey.
Answer: Accroding to the formula
              Average speed = 2X35X25/60
                                    = [A= 35 km/s, B= 25 km/s]
                                    = 70X25/60 = 175/6
                                  = 29.16 km/h.

   Technique 2:
              When a person reaches a certain distance ‘a’ he gets t1 time late and when he increases his speed by ‘b’ to cover the same distance, then he still gets late by t2 time. In case, the distance is calcuated by
D = (t1 – t2)(a+b) a/b

Example: A boy walking at a speed of 20 km/h reaches his school 30 min late. Next time he increases his speed by 4 km/h but still he is late by 10 min. find the distance of the school from his home?
Answer:Given data a=20 km/h, b= 4 km/h, t1= 30 min, t2 = 10 min
          According to the formula,
                Required distance = (t1- t2)(a+b)a/b
                                        = (30-20)/60(20+4)20/4
                                        = 20/60X24X20/4
                                        = 5X8 = 40 km.

Technique 3:
    When two persons A and B travel from points P to Q, a distance of D with speeds ‘a’ and ‘b’, respectively and B reaches Q first, returns immediately and meets A to R, then
               Distance traveled by A (from points P to R) = 2X D(a/a+b)
               Distance traveled by B (PQ+QR)     = 2XD (b/a+b)
Example: ramu and monu travel from Pto Q, a distance of 42 km, at 6 km/h and 8 km/h, respectively. Monu reaches Q first and returns immediately and meets ramu at R. find the distance from points P to R.
Answer:  here, D= 42 kms, a= 6 km/h, b= 8 km/h
             According to the formula,
             Distance travelled by ramu  = PR = 2Dxa/a+b
                                                      = 2X42X6/6+8
                                                      = 2X42X6/14
                                                   = 2X3X6 = 36 km

Technique 4:
               A policeman sees a thief at a distance of d. he starts chasing the thief who is running at a speed of ‘a’ and policeman is chasing with a speed of ‘b’ (b>a). in this case, the distance covered by the thief when he is caught by the policeman, is given by
Example: A policeman sees a chain snatcher at a distance of 50 m. He starts chasing the chain snatcher who is running with a speed of 2 m/s while the policeman chasing him with a speed of 4 m/s. find the distance covered by the chain snatcher when he is caught by the policeman.
Answer: here, d= 50m, a= 2 m\s, b= 4m/s
            According to the formula, required distance = d(a/b-a)
                                                                           = 50X 2/4-2

                                                                    ans= 50 m
Powered by Blogger.