Time
and Distance
Distance
:
The length of the path travelled by an
object or a body or a person between two places is known as distance. It is
measured in meters or kilometers.
Speed
:
The distance travelled by any object
or person in unit time is known as the speed of the object or speed of a
person. It is measured in meter per second or kilometer per hour.
Speed =
Distance
Time
Distance = Speed x Time
Time =
Distance
Speed
Example: Sameera
travelled a distance of 95 kilometres in 5 hours.
Therefore distance travelled by
Sameera in 1 hour =
95
5
= 19 km
Hence,
the speed of Sameera = 19kmph
Conversion of Units :
From
km/h to m/s :
To convert the speed of an object from
kmph to mps, multiply the speed by
5
18
.
x kmph = x x
5
18
mps
Example : 72 kmph = 72 x
5
18
= 20 mps
From
m/s to km/h.
To convert the speed of an object from
mps to kmph, multiply the speed by
18
5
.
x mps= x x
18
5
kmph
Example : Convert 30 mps
into kmph
30 x
18
5
= 108 kmph
Average
Speed :
If a certain
distance is covered in parts in different time periods, then
Average speed=
Total distance covered
Total time taken
Example:
A person travels 80 km in 6 hours and the next 30
km in 5 hours. What is his average
speed?
Total distance covered = (80 km + 30 km) = 110 km
Total time taken = (6 hours + 5 hours) = 11 hours.
Average Speed =
Total distance covered
Total time taken
=
110
11
= 10 kmph
Average
Speed when an object travels equal distances with different speeds:
1.
If a person covers two equal distances with the speed of x and y
units respectively, then the average
speed of the man for complete journey =
2xy
(x+y)
Example: John covers half of the
distance with speed of 40 kmph and the remaining half of the distance with
speed of 60 kmph. What is his average speed?
Answer : He travelled two equal
distance with speeds 40kmph and 60kmph
Average Speed =
2 x 40 x 60
(40+60)
= 48 kmph
2.
A person travels 3 equal distances with speeds x, y and z units,
then his average speed =
3xyz
(xy+yz+zx)
Example : Sudheer travels 1/3rd of his journey at 10
km/h , next 1/3rd at 30km/h and remaining 1/3rd at 60km/h. What is his average speed during
the journey?
a)15 km/h b)20 km/h c)25km/h d)30km/h
Answer :Sudheer travels 3 equal distances at speeds of 10 kmph, 20
kmph and 30 kmph
Average Speed =
3xyz
(xy+yz+zx)
=
(3 x 10 x 30 x 60 )
(10 x 30) + (30 x 60) + (60 x 10)
= 20 kmph
Concept of Relative Speed :
Objects moving in the same direction: If two objects
are moving in the same direction at
speeds of x and y, then their
relative speed = (x-y)
For example, if the two bikes A and B
move in the same direction at speeds of 50 kmph and 40 kmph , then the relative
speed of A with respect to B is (50-40)=10 kmph.
Example : Ravi and Raju
start walking in the same direction at 12 km/h and 10 km/h, respectively. In how
many hours will they be 16km apart?
a)4 hours b)5 hours c)6
hours d)8 hours
Answer : Time =
Distance
Speed
Here both are moving in the same direction, so the relative speed
is (12-10) = 2 kmph
Time =
16
2
= 8 hours
Objects are moving in the opposite direction : If two objects are moving in opposite directions at speeds of x
and y, then their relative speed = (x+y).
If two cars are travelling towards each other at speeds of 30 kmph
and 40 kmph respectively, then their relative speed = (30+40) = 70 kmph.
Example : Sameera and Sravani walking in
opposite directions at 12km/h and 10
km/h, respectively. In how many hours will they be 66 km apart?
a)6 hours b)33 hours c)3
hours d)5 hours
Answer : Sameera and Sravani are walking in the opposite
direction , their relative speed is the sum of their speeds = (12+10) =22 kmph
Time =
Distance
Time
=
66
22
= 3 hours
Note : The ratio of
speeds of two objects is a:b, then to cover the same distance, the ratio of
time taken will be b:a
Example : The ratio of the
speeds of two persons to cover a distance is 4:5, then the ratio of time taken
by them to cover the same distance will be 5 :4.
Example: The
ratio between the speeds of A and B is 5 :7, and A takes 35 minutes to cover a
distance. In what time does B cover the same distance?
a)10
min b)15 min c)25 min d)30min
Answer :
The ratio of between the speeds of A and B is 5:7
Then ratio of the times taken by A and B =
7:5
Time taken by A to cover a distance is 7x =
35 minutes
Therefore, time taken by B to cover same
distance = 5x = 5x5 = 25 minutes