SPEED
TIME AMD DISTANCE
Formula for speed , time and
distance
1.
Speed = Distance traveled / time taken
2.
Distance = speed x time
3.
Time = distance/speed
Proportionality concept
1.
If the distance traveled is the same at two
different speed s1 and s2 and at different time t1 and t2 respectively time
then
s1t1
= s2t2 or s1/t2 s2/t1
It means if the
speed is doubled then the time taken is halved or vice versa , keeping the
distance traveled the same.
2.
If the time taken for the entire journey is the
same then,
d1/s1 =d2/s2
It means if the distance is doubled then the speed would be doubled also
and vice versa keeping the same time travelled for.
3.
If the speed is same then
d1/t1=d2/t1
That is if the distance traveled is doubled then the time taken will be
doubled also keeping the same speed.
Calculation for average speed
By definition,
Average speed =
total distance travelled/total time taken
The questions given in
examinations are of three different types.
1. Distances traveled and time taken to
travel those distances are given.
Then the average speed is calculated as
Average speed = (d1+d2+d3+….+dn)/(t1+t2+t3+…+tn)
Where d1 is the distance travelled in time t1 and d2 is the distance
travelled in time t2 and so on.
2.
When different speeds and times for which the
speed stayed constants are given.
Then the average speed is given by
Average speed = (s1t1+s2t2+s3t3+….+sntn)/(t1+t2+t3+…+tn)
Where s1 is the speed at which the object travelled for time t1 and s2 is
the speed at which the object travelled for time t2 and so on.
3.
When the distances travelled and the speeds at
which those distances travelled are given
Average speed = (d1+d2+…+dn)/(d1/s1 + d2/s2 + …+ dn/sn)
Where d1 is the distance travelled at speed s1 and d2 is the distance
traveled at speed s2 and so on.
Relative speed
When speeds of moving object are
measured relative to one other then the concept of relative speed arises.
1.
When two bodies are moving along a same line in
the same direction then the speed of the first body relative to the second body
is
(U –
V)
This is the speed the first body appears to be moving as compared to the
second body.
2.
When two bodies are moving along a same line in
different directions then the speed of the first body relative to the second
body is
(U +
V)
This is the speed the first body appears to be moving as compared to the
second body.
Important concepts
1.
Speed of passing
a. Speed
of passing a stationary object which is small is size is the speed of the
moving object.
b. Speed
of passing a moving object is the relative speed of the moving objects
2.
Distance covered while passing
a. If
the length of the object, which a large moving objet such as train is passing,
then the distance travelled is the train itself.
b. If
the two large objects, such as trains or ships, are passing each other then the
total distance traveled is the sum of the two bodies.
Useful concepts
1.
Time after meeting
If two bodies,A and B are moving towards each other starting from point P and Q with speed S1 and
S2 and they meet at certain point and then continue with their journey towards
points Q and P respectively. Then after meeting the train A takes ta time to
reach Q and train Q takes tb time to reach point P, and their speed were sa
and sb respectively then ,
Sa/Sb= √tb/√ta
2.
Again if two bodies are travelling towards each
other and meet at some point, then the time taken is the same for both the
bodies, then
da/db = sa/sb
where da is the distance travelled at speed sa for the first body and db
and sb are the distance travelled by body b during the same time.
Boats and Streams
1.
Downstream speed of the boat = Sd= S + s
Where S is the speed of the boat and s is the speed of the current.
2.
Upstream speed of the boat = Su = S – s
3.
If Sd and
Su are the speed of the boat in downstream and upstream then
i.
The speed of boat in still water = (Sd + Su)/2
ii.
The speed of stream = (Sd - Su)/2
Circular motion
1.
When the two bodies are going in the same
direction
a. The
speed to consider would be the relative speed of the two objects. i.e. U-V
b. The
distance covered by the faster body when it meets the slower body first time is
one complete circle more than the slower body.
Time taken to meet
for the first time = D/(U-V) where D is the circumference of the circular path
2.
When the two bodies are going in the opposite
direction around a circular path then
a. the
relative speed would be U +V
b. the
distance travelled when they first meet would be equal to the circumference of
the circular path.
Time taken to meet
for the first time = D/(U+V) where D is the circumference of the circular path.
Time taken to meet at the
starting point for both the bodies is the LCM of the times taken by each body
to complete one round, that is the LCM of the D/U and D/V. It is applicable for
both the conditions i.e. when they move in the same direction and in opposite
direction.
CLOCKS
2.
The speed of the hour hand = 360/(12x 60 ) = ½
degrees per minute.
3.
The relative speed of the minute hand and hour
hand is 6 – ½ = 5.5 degrees per minute
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