Maths for UPSC, SSC, IBPS : Time Speed

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This chapter provides an overview of concepts
of time, speed and distance. These concepts are
essential for solving aptitude questions. Its
variations are seen in several formats such as
boats, trains, streams, etc.
CHAPTER OVERVIEW
SPEED s
TIME t
DISTANCE d
x

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Distance is the overall displacement of the body
during the motion. Its units are in cm, m, km,
etc.
Speed is rate at which distance is covered per
unit time during the motion. Its units are km/hr,
m/s, cm/s, etc.
Time is the time duration over which the motion
has occurred. Its units can be s or seconds,
min, hr, day, week, etc.
Distance
Speed
Time
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Properties

1. If speed is constant, distance is
proportional to time
If speed is same (say 2 km/hr), more distance is
travelled if time is more i.e 2 km in 1 hr , 4 km
in 2 hrs and so on....
2. If time is constant, speed is proportional to
distance
If time is same (say 2 hrs), more distance is
travelled if speed is more i.e 2 km by 2 km/hr, 4
km by 4 km/hr and so on....
2. If distance is constant, speed is inversely
proportional to time
If distance is same (say 2 km), more speed taken
would take less time , i.e 1 hr by 2km/hr , 2hrs
by 1 km/hr and so on.....
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Properties
4. To convert km/hr to m/s multiply by 5/18

To convert m/s to km/hr multiply by 18/5
5. If same distance is covered for different
journeys with two different speeds i.e S1 for A
to B and S2 for B to A then average speed
is given by
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Relative Speed is speed of one moving body
relative to another moving body. For same
direction their speeds are subtracted while for
opposite direction they add up.
Acceleration is simply rate of change of speed
i.e. change of speed per unit time. A decrease in
speed is know as deceleration (negative
acceleration).

Acceleration
Relative Speed
For same direction
For opposite direction
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Application on Trains
Train crossing an object without length (a pole)
Train crossing an object withlength (a platform)
Train crossing a moving object without length (a
pole)
Sr is relative speed
Train crossing a moving object with length (a
platform)
same direction
Opposite direction
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Application on boats
1. If speed of boat in still water is S1 km/hr
and speed of stream is S2 km/hr then the speed of
boat in the stream is given as relative speed of
the two.
Speed downsteam means speeds add up.
As in downstream movement, stream provides push
to the boat and increases its speed.
Speed upstream means speeds are subtracted.
As in upstream movement, stream provides
resistance to the boat and decreases its speed.
2. If speed of boat downstream is x km/hr and
speed upstream is y km/hr (xgty) then the speed of
boat in still water and speed of stream are
speed of stream
speed of boat in still water
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