Velocity of a particle is given by v is equal to 3 minus speed the distance travelled by the particle in first second
Answers
Rectilinear motion is a motion of a particle or object along a straight line.
Position is the location of object and is given as a function of time
s
(
t
)
or
x
(
t
)
.
Velocity is the derivative of position:
v
=
d
x
d
t
.
Acceleration is the derivative of velocity:
a
=
d
v
d
t
.
The position and velocity are related by the Fundamental Theorem of Calculus:
t
2
∫
t
1
v
(
t
)
d
t
=
x
(
t
)
|
t
2
t
1
=
x
(
t
2
)
−
x
(
t
1
)
,
where
t
1
≤
t
≤
t
2
.
The quantity
x
(
t
2
)
−
x
(
t
1
)
is called a displacement. The displacement is represented by the area under the graph of the velocity
v
(
t
)
.
Displacement is the area under the velocity graph
Figure 1.
Similarly, since acceleration is the rate at which the velocity changes, we have
t
2
∫
t
1
a
(
t
)
d
t
=
v
(
t
)
|
t
2
t
1
=
v
(
t
2
)
−
v
(
t
1
)
,
where the quantity
v
(
t
2
)
−
v
(
t
1
)
is the net change in velocity in the time interval
t
1
≤
t
≤
t
2
.
Speed
|
v
(
t
)
|
is the absolute value of velocity, i.e. speed is always positive.
The average speed
v
a
v
is defined as
v
a
v
=
total distance traveled
total time
.
The total distance
s
a particle travels between time
t
1
and time
t
2
is given by
s
=
t
2
∫
t
1
|
v
(
t
)
|
d
t
.