Bombay Cambridge Gurukul Time Distance and Speed MATHEMATICS

Bombay Cambridge Gurukul 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 ¨ Train goes past a pole ¨ Time, distance and speed in daily life ¨ Check It Out

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…)

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

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

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

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

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

Easy way to Remember Conversion 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 BACK

Important Formulae DISTANCE = SPEED X TIME SPEED = TIME = DISTANCE TIME DISTANCE SPEED Easy Formula: If you Way know to any. Remember of the two ofthe Distance three variables, (distance, Ispeed stay in (DST thethe order and. DSTREET. time) you can findare out in what otheras oneinis. the Distance Formula. ) BACK

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

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

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

III) CALCULATE SPEED FROM TIME AND DISTANCE Enter Time 2 hrs Enter Distance 45 min 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 45 min = 45 hr 60 4 ( Contd……. )

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

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

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 44 4 hrs 44 hrs 352 km = 8 hrs + = 8 = = 5 5 5 40 km/hr 5 12 4 = 8 hrs and X 60 min 5 1 = 8 hrs and 48 min The bus started at 20. 00 hrs and travelled for a period of 8 hrs 48 min. (Contd…)

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. hrs 28 min 48 24 00 4 48 = 4 hrs and 48 min The bus reached Nasik early morning the next day at 4 hours and 48 minutes. BACK

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…)

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 Conversion: Time = 20 sec 2 6 36 km/hr = 36 x 5 = 10 m/sec 18 3 1 DISTANCE = SPEED X TIME Distance = 10 m/sec x 20 sec BACK = 200 m

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

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

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