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MATHEMATICS STANDARD : VII

Time, Distance and Speed. MATHEMATICS STANDARD : VII. Contents. Time, distance and speed – concept Units of Measurement Conversion Important formulae Calculate distance using formula Calculate time using formula Calculate speed using formula Word Problems

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MATHEMATICS STANDARD : VII

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  1. Time, Distance and Speed MATHEMATICS STANDARD : VII

  2. Contents • Time, distance and speed – concept • Units of Measurement • Conversion • Important formulae • Calculate distance using formula • Calculate time using formula • Calculate speed using formula • Word Problems • Train goes past a pole • Time, distance and speed in daily life • Check It Out

  3. Time, Distance & Speed- Concept Home Tree In the picture above the girl is going really fast. She catches up and passes the boy. Can you say who is slower? The boy is slower than the girl. Can you say why is the boy slower than the girl? The boy is slower than the girl because the boy takes more time to cover the same distance. (Contd…)

  4. We can also say that the speed of boy is less than that of the girl. When a person covers a given distance in a given time then the person is said to be in motion and the rate with which he/she moves is called speed. BACK

  5. Units of Measurement The units of measurement of distance are km, m, cm etc. The units of measurement of time are hour (hr), minute (min), second (sec). The units of measurement of speed are km/hr and m/sec, cm/sec etc. NOTE: The units of time and distance determine the unit of measurement of speed. BACK

  6. 1 1000 km 1 m = 1 60 ´ 60 hr \ 1 sec = Conversion 1000 m = 1 km 1 hr = 60 min 1 min = 60 sec \ 1 hr = 60 ´ 60 sec (Contd…)

  7. 1000 m 60 x 60 sec 5 m 18 sec e.g. 90km/hr = 90 x = 90 x 1) Changing the speed given in km/hr into m/sec. 5 3 5 10 2 1 90 km/hr = 25 m/sec (Contd…) 18

  8. ¸ 1 60 x 60 hr e.g. 50m/sec = 50 1000 km 50 1000 x 60 x 60 = 60 x 60 1000 \ 50m/sec = 50 x = 50 x 18 km 5 hr 2) Changing the speed given in m/sec into km/hr. 3 5 10 1 50m/sec = 180km/hr

  9. To convert the speed given in km/hr into m/sec, multiply the given speed by 5 18 To convert the speed given in m/sec into km/hr, multiply the given speed by 18 5 Easy way to Remember Conversion BACK

  10. DISTANCE SPEED TIME = Important Formulae DISTANCE = SPEED X TIME DISTANCE TIME SPEED = Easy Way to Remember the Distance Formula: I stay in DSTREET. (DST are in the order as in the Distance Formula.) If you know any of the two of the three variables, (distance, speed and time) you can find out what the other one is. BACK

  11. Enter Speed 40 m/sec Enter Time = X 400 m = I) CALCULATE DISTANCE FROM SPEED AND TIME 10 sec DISTANCE = SPEED X TIME 10 sec 40 m/sec BACK

  12. Enter Distance 30 m Enter Speed 27 km/hr 5 18 = 27 x 15 2 m/sec = II) CALCULATE TIME FROM DISTANCE AND SPEED Distance & speed are not in the same unit of measurement, so conversion is required. Conversion: Speed = 27km/hr 3 2 ( Contd…….)

  13. DISTANCE SPEED TIME = 2 15 = 30 X 30 m = 15/2 m/sec 2 = 4 sec. 1 TIME = 4 seconds BACK

  14. Enter Time 45 min 2 hrs Enter Distance 45 hr 45 min = 60 III) CALCULATE SPEED FROM TIME AND DISTANCE 132 km Time is given in both hour and minute so this can be converted into hour. Conversion : Time = 2 hrs 45 min OR Time = 2 hrs + 45 min 3 4 ( Contd…….)

  15. 3 hr 45 min = 4 3 hr \ 2 hrs + 45 min = 2 hr + 4 8 + 3 11 hr hr = = 4 4 (Contd…….) (Contd…….)

  16. 132 km 11/4 hr DISTANCE TIME 4 11 SPEED = = 132 X = 12 1 SPEED = 48 km/hr BACK

  17. 4 4 44 44 hr hrs = 8 hrs + = 8 hrs 352 km 5 5 = = 5 40 km/hr 5 12 4 5 X 60 min = 8 hrs and 1 Word Problems The distance between Pune and Nasik is 352 km. A bus running at the speed of 40 km/hr left Pune at 20.00 hrs. What time will it reach Nasik? TIME = DISTANCE ¸ SPEED = 8 hrs and 48 min The bus started at 20.00 hrs and travelled for a period of 8 hrs 48 min. (Contd…)

  18. min hrs 2 8 4 8 2 4 0 0 4 8 4 Contd… \ the bus reached at 20.00 hrs + 8.48 hrs = 28.48 hrs To find the time of the day according to the 24 hours system, let us subtract 24 from 28.48 . = 4 hrs and 48 min The bus reached Nasik early morning the next day at 4 hours and 48 minutes. BACK

  19. TRAIN GOES PAST A POLE Q. A train running at the speed of 36 km/hr goes past a pole in 20 seconds. Find the length of the train. What does the phrase “train goes past a pole mean”? This means that the train has to travel a distance equal to its length to go past the pole. Hence, the time required to go past a pole is the same as the time required to travel a distance equal to the train’s length. (Contd…)

  20. 5 18 = 36 x 10 m/sec = SOLUTION: The length of the train will be equal to the distance travelled in the given time with the same speed. Speed =36 km/hr Time =20 sec Conversion: 2 6 36 km/hr 3 1 DISTANCE = SPEED X TIME Distance = 10m/sec x 20 sec BACK = 200 m

  21. Time, Distance and Speed in Daily Life Speed, time and distance is one of the basic tools a sailor uses in navigation. Using these simple formulae he can predict the time of arrival, the speed of travel or the distance he has to cover. In athletic events and elimination rounds speed, distance and time play a major role in the making and breaking of records. The departure and arrival of aeroplanes, trains and buses depends on calculations involving speed, time and distance. BACK

  22. 1 km 1 m = 1 ___ ´ ___ 1 sec = hr Time = Distance Speed = Distance To convert the speed given in km/hr into m/sec, multiply the given speed by 5 Fill in the blanks and complete the following: 18 60 1 hr = 60 ´______ sec Check It Out 1000 Time Speed Speed Distance = ___________ X Time BACK 60 60

  23. The End

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