formula of
S1=S2=S; equal distance with different velocities p
Answers
Answer:
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Explanation:
Important Formulas - Time and Distance
1. Basics
speed
=
distance
time
distance
=
speed
×
time
time
=
distance
speed
2. Convert kilometres per hour(km/hr) to metres per second(m/s)
x
km/hr
=
x
×
5
18
m/s
View Proof
3. Convert metres per second(m/s) to kilometres per hour(km/hr)
x
m/s
=
x
×
18
5
km/hr
View Proof
4. Average Speed
If an object covers a certain distance at
x
kmph and an equal distance at
y
kmph, the average speed of the whole journey
=
2
x
y
x
+
y
kmph
View Proof
5. Relation Between Distance, Speed and Time
(5.1) Speed and time are inversely proportional (when distance is constant)
⟹
speed
∝
1
time
(when distance is constant)
(5.2) If the ratio of the speeds of A and B is
a
:
b
,
then, the ratio of the time taken by them to cover the same distance is
1
a
:
1
b
=
b
:
a
View Proof
(5.3) Assume two objects A and B start at the same time in opposite directions from P and Q respectively. After passing each other, A reaches Q in
a
seconds and B reaches P in
b
seconds. Then,
Speed of A : Speed of B
=
√
b
:
√
a
View Proof
(5.4) An object covered a certain distance at a speed of
v
kmph. If it had moved
v
1
kmph faster, it would have taken
t
1
hours less. If it had moved
v
2
kmph slower, it would have taken
t
2
hours more. Then,
v
=
v
1
v
2
(
t
1
+
t
2
)
v
1
t
2
−
v
2
t
1
kmph
x
=
v
t
1
(
1
+
v
v
1
)
km
Special Case:
If
t
1
=
t
2
,
v
=
2
v
1
v
2
v
1
−
v
2
kmph
View Proof
6. Relative Speed
(6.1) If two objects are moving in the same direction at
v
1
m/s and
v
2
m/s respectively where
v
1
>
v
2
,
then their relative speed
=
(
v
1
−
v
2
)
m/s
(6.2) Consider two objects A and B separated by a distance of
d
metre. Suppose A and B start moving in the same direction at the same time such that A moves towards B at a speed of
a
metre/second and B moves away from A at a speed of
b
metre/second where
a
>
b
.
Then,
relative speed
=
(
a
−
b
)
metre/second
time needed for A to meet B
=
d
a
−
b
seconds
View Proof
(6.3) If two objects are moving in opposite directions at
v
1
m/s and
v
2
m/s respectively, then their relative speed
=
(
v
1
+
v
2
)
m/s
(6.4) Consider two objects A and B separated by a distance of
d
metre. Suppose A and B start moving towards each other at the same time at
a
metre/second and
b
metre/second respectively. Then,
relative speed
=
(
a
+
b
)
metre/second
time needed for A and B to meet each other
=
d
a
+
b
secondsImportant Formulas - Time and Distance
1. Basics
speed
=
distance
time
distance
=
speed
×
time
time
=
distance
speed
2. Convert kilometres per hour(km/hr) to metres per second(m/s)
x
km/hr
=
x
×
5
18
m/s
View Proof
3. Convert metres per second(m/s) to kilometres per hour(km/hr)
x
m/s
=
x
×
18
5
km/hr
View Proof
4. Average Speed
If an object covers a certain distance at
x
kmph and an equal distance at
y
kmph, the average speed of the whole journey
=
2
x
y
x
+
y
kmph
View Proof
5. Relation Between Distance, Speed and Time
(5.1) Speed and time are inversely proportional (when distance is constant)
⟹
speed
∝
1
time
(when distance is constant)
(5.2) If the ratio of the speeds of A and B is
a
:
b
,
then, the ratio of the time taken by them to cover the same distance is
1
a
:
1
b
=
b
:
a
View Proof
(5.3) Assume two objects A and B start at the same time in opposite directions from P and Q respectively. After passing each other, A reaches Q in
a
seconds and B reaches P in
b
seconds. Then,
Speed of A : Speed of B
=
√
b
:
√
a
View Proof
(5.4) An object covered a certain distance at a speed of
v
kmph. If it had moved
v
1
kmph faster, it would have taken
t
1
hours less. If it had moved
v
2
kmph slower, it would have taken
t
2
hours more. Then,
v
=
v
1
v
2
(
t
1
+
t
2
)
v
1
t
2
−
v
2
t
1
kmph
x
=
v
t
1
(
1
+
v
v
1
)
km
Special Case:
If
t
1
=
t
2
,
v
=
2
v
1
v
2
v
1
−
v
2
kmph
View Proof
6. Relative Speed
(6.1) If two objects are moving in the same direction at
v
1
m/s and
v
2
m/s respectively where
v
1
>
v
2
,
then their relative speed
=
(
v
1
−
v
2
)
m/s
(6.2) Consider two objects A and B separated by a distance of
d
metre. Suppose A and B start moving in the same direction at the same time such that A moves towards B at a speed of
a
metre/second and B moves away from A at a speed of
b
metre/second where
a
>
b
.
Then,
relative speed
=
(
a
−
b
)
metre/second
time needed for A to meet B
=
d
a
−
b
seconds
View Proof
(6.3) If two objects are moving in opposite directions at
v
1
m/s and
v
2
m/s respectively, then their relative speed
=
(
v
1
+
v
2
)
m/s
(6.4) Consider two objects A and B separated by a distance of
d
metre. Suppose A and B start moving towards each other at the same time at
a
metre/second and
b
metre/second respectively. Then,
relative speed
=
(
a
+
b
)
metre/second
time needed for A and B to meet each other
=
d
a
+
b
seconds