MATHEMATICS STANDARD : VII Time, Distance and Speed Time, Distance and Speed.
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Transcript of MATHEMATICS STANDARD : VII Time, Distance and Speed Time, Distance and Speed.
MATHEMATICSMATHEMATICS
STANDARDSTANDARD : VII : VII
Time, Distance and SpeedTime, Distance and Speed
Contents 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
In the picture above the girl is going really fast. She catches up and passes the boy.Can you say who is slower?
Time, Distance & Speed- Concept
Time, Distance & Speed- Concept
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…)
Home Tree
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.
We can also say that the speed of boy is less than that of the girl.
BACK
NOTE: The units of time and distance determine the unit of measurement of speed.
Units of MeasurementUnits 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.
BACK
1000 m = 1 km
1 hr = 60 min
1 min = 60 sec
1 hr = 60 60 sec
1 m = 1 1000
km
1 sec =1
60 60 hr
ConversionConversion
(Contd…)
= 90 x 5 m
18 sec
1) Changing the speed given in km/hr into m/sec.
e.g. 90km/hr = 90 x 1000 m
60 x 60 sec
3
5
2
10
1
5
90 km/hr = 25 m/sec
(Contd…)
50m/sec = 50 x 60 x 60 1000
2) Changing the speed given in m/sec into km/hr.
50m/sec = 180km/hr
5
3
e.g. 50m/sec = 160 x 60
hrkm 501000
x 501000
60 x 60=
= 50 x
18 km 5 hr1
10
To convert the speed given in km/hr into
m/sec, multiply the given speed by 518
Easy way to Remember Conversion
Easy way to Remember Conversion
BACK
To convert the speed given in m/sec into
km/hr, multiply the given speed by 18 5
DISTANCE TIME SPEED =
DISTANCE SPEED
TIME =
If you know any of the two of the three variables, (distance, speed and time) you can find out what the other one is.
Easy Way to Remember the Distance Formula: I stay in DSTREET. (DST are in the order as in the Distance Formula.)
Important FormulaeImportant Formulae
DISTANCE = SPEED X TIME
BACK
Enter Speed
I) CALCULATE DISTANCE FROM SPEED AND TIME
Enter Time
40 m/sec
DISTANCE = SPEED X TIME
10 sec
= X40 m/sec 10 sec
= 400 m
BACK
= 27 x 518
II) CALCULATE TIME FROM DISTANCE AND SPEED
Enter Distance
Enter Speed
30 m
27 km/hr
Conversion:
Speed = 27km/hr
3
Distance & speed are not in the same unit of measurement, so conversion is required.
15 2
m/sec=
2( Contd…….)
=30 m
15/2 m/sec
= 30 X 2151
2= 4 sec.
TIME = 4 seconds
BACK
DISTANCE SPEEDTIME =
III) CALCULATE SPEED FROM TIME AND DISTANCE
Enter Time
Enter Distance
2 hrs 45 min
132 km
Conversion : Time = 2 hrs 45 min
4560
hr45 min =
Time is given in both hour and minute so this can be converted into hour.
4
3
Time = 2 hrs + 45 min
OR
( Contd…….)
34
hr45 min =
2 hrs + 45 min 4
= 2 hr + 3 hr
(Contd…….)
= 8 + 3 hr4
= 11 hr4
(Contd…….)
1
DISTANCE TIMESPEED =
=132 km
11/4 hr
411= 132 X
12
SPEED = 48 km/hr
BACK
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
352 km
40 km/hr=
5
44
=44
5hrs = 8
4
5hrs 8 hrs +=
4
5hr
= 8 hrs and X 60 min45
1
12= 8 hrs and 48 min
The bus started at 20.00 hrs and travelled for a period of 8 hrs 48 min.
(Contd…)
Word ProblemsWord Problems
the bus reached at 20.00 hrs + 8.48 hrs = 28.48 hrs
= 4 hrs and 48 min
Contd…
To find the time of the day according to the 24 hours system, let us subtract 24 from 28.48 .
hrs min
2 8 4 8
2 4 0 0
4 4 8
The bus reached Nasik early morning the next day at 4 hours and 48 minutes.
BACK
TRAIN GOES PAST A POLETRAIN 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.
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.
What does the phrase “train goes past a pole mean”?
(Contd…)
SOLUTIONSOLUTION::
The length of the train will be equal to the distance travelled in the given time with the same speed.
DISTANCE = SPEED X TIMEDISTANCE = SPEED X TIME
Speed = 36 km/hr
Distance = 10m/sec x 20 sec
= 200 m
Time = 20 sec
= 36 x 518
10 m/sec=3
6
1
2
36 km/hr
Conversion:
BACK
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.
Time, Distance and Speed in Daily Life
Time, Distance and Speed in Daily Life
BACK
1 hr = 60 ______ sec1 m = 1 km1000
60
Fill in the blanks and complete the following:
Fill in the blanks and complete the following:
To convert the speed given in km/hr into m/sec,
multiply the given speed by 518
Speed = Distance Time = DistanceSpeedTime
Distance = ___________ X Time
1 sec = 1 ___ ___
hr
60 60
Speed
BACK
The End