Time Distance

MATHEMATICSMATHEMATICS

STANDARDSTANDARD : VII : VII

Bombay Cambridge GurukulBombay Cambridge Gurukul

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

Created byDepartment of ResearchDepartment of Research

The End