Distance covered per unit time is called
speed. .
i.e., Speed = Distance/time or .
Distance = Speed x time or
Time = Distance/speed
- If two
bodies travel with the same speed, Distance covered m Time (Direct Variation). .
- If two
bodies travel for the same period of time, Distance covered m Speed (Direct Variation). .
- If two
bodies travel in the same distance, Time m
(Inverse
Variation)
Distance is normally measured in km, metres
or miles; Time in hours or seconds and Speed in Km/hr (also denoted by kmph),
miles/hr (also denoted by mph) or metres/second (denoted by m/s). .
To convert speed in kmph to m/sec, multiply
it with (5/18). .
To convert speed in m/sec to kmph, multiply
it with (18/5). .
Relative Speed
The speed of one (moving) body in relation to
another moving body is called the relative speed for these two bodies. If two
bodies are moving in the same direction, the relative speed is equal to the
difference of the speeds of the two bodies. If two bodies are moving in
opposite direction, the relative speed is equal to the sum of the speeds of the
two bodies. .
Average Speed
Average speed of a body travelling at
different speeds is NOT EQUAL to the average of the speeds but is defined as
follows:
Average Speed = 
Worked out examples
example.1
A person can cover certain distance in 8
hours at a speed of 50 kmph. At what speed must he travel to cover the distance
in 5 hours? .
Solution
Distance
= Speed x time = 50 x 8
= 400 km
400 = speed x 5
speed = 80 kmph
example.2
A train travelled for 9 hours. It travelled
the first half of the distance at 12 kmph and remaining distance at 15 kmph.
Find the distance. .
Solution
Let the
distance be x km. .
Time taken = 
9x = 120 x 9
&⇒ x = 120 km
example.3
A train,
300 m long is moving at 54 kmph. How long does it take .
(a) to cross an electric pole?
(b) to cross a platform 150 in long?
(c) to cross a person moving in the same
direction at 18 kmph?
(d) to cross a person moving in opposite
direction at 18 kmph?
(e) to cross another train, 300 m long,
running at 36 kmph in opposite direction?
(f) to cross another train, 300 m long,
running at 36 kmph in the same direction?
Solution
Speed of the train = 54 x 
= 15m/s
(a) speed = 15 m/s; distance = 300 m
so time = 
= 20 sec.
(b) Distance = 300 + 150 = 450
Time = 
= 30 sec
(c) Speed of the train relative to the
man
= 54 - 18 = 36 kmph
= 36 x m/s = 10
m/s
Time = 
= 30 sec.
(d) Speed of the train relative to the
man
= 54 + 18 = 72 kmph
= 72 x m/s = 20
m/s
Time = 
= 15 sec
(e) Total distance = 300 + 300
= 600 m
relative speed = 54 + 36 =
90 kmph
= 90 x = 25 m/s
Time = 
= 24
sec.
(f) Total distance = 300 + 300 = 600 m
relative speed = 54 - 36 =
18 kmph
= 18 x = 5 m/s
Time = 
= 120
sec .
EXAMPLE.4
A person covered 280 km. He covered 
of the
distance at 70 kmph and the remaining distance at 35 kmph. What is the average
speed of the person?
Solution
of 280 =
x 280 = 210
km
Time taken to cover 210 km is
= 3
hours.
Time taken to cover remaining
70 km = 
= 2
hours
Average speed = 
= 
= 56
kmph
example.5
Train T crosses a bridge 100 m long in 21
seconds. It crosses another bridge 220 m long in 33 seconds. Find its speed. .
Solution
Let the
speed of T be S m/sec. Let its length be L m. .
= 21 and
= 33.
&⇒ L = 21S - 100 and L = 33S - 220
&⇒ L= 21S - 100 = 33S - 220
&⇒ 12S = 120
&⇒ S = 10. .
