Velocity &
Acceleration – Class 8
1.
What
do you mean by reference point or origin?
-
To
define state of the rest or motion of a body, a fixed point or a certain point
or a considering point is required, which is known as reference point or
origin.
2.
What
do you mean by rest?
-
The
body which is not changing its position with respect to a reference point, then
the body is known as in the rest. For example: house, tree etc.
3.
What
do you mean by motion?
-
The
body which is changing its position with respect to a reference point, then the
body is known as in the motion. For example: moving vehicle etc.
4.
Why
rest and motion are called relative terms?
-
Rest
and motion need comparison with a reference point to explain. So they are
called relative terms.
5.
What
do you mean by uniform motion?
-
If
a body covers equal distance in each and every unit time, then such motion is
known as uniform motion. For example: motion of needle of watch, motion of fan,
motion of machines etc.
6.
What
do you mean by non-uniform motion?
-
If
a body doesn’t cover equal distance in each and every unit time, then such
motion is known as non-uniform motion. For example: motion of a running man,
bicycle etc.
7.
What
do you mean by uniformly accelerated motion?
-
If
velocity of a body is increasing or decreasing constantly in per unit time,
then the motion is known as uniformly accelerated motion. For example: a body
falling towards the center of the earth, a stone thrown vertically upward, etc.
8.
What
do you mean by scalar quantity? Give examples.
-
The
quantities which have only magnitude but not the direction are called scalar
quantities. For example: speed, mass, length, time etc.
9.
What
do you mean by vector quantity? Give example.
-
The
quantities which have both magnitude and direction are called vector
quantities. For example: velocity, force, displacement etc.
10. Length
is called a scalar quantity, why?
-
Because
length consists only magnitude not the direction. So length is called a scalar
quantity.
11. Velocity
is called as a vector quantity, why?
-
Because
velocity consists both magnitude and direction. So velocity is called vector
quantity.
12. Write down the differences
between vectors and scalars.
-
Following
are the differences between vectors and scalars.
Scalars
|
Vectors
|
-These
have magnitude only.
|
-
These have magnitude as well as directions.
|
- Speed, mass,
times etc. are some examples of scalars.
|
-
Velocity, force, displacement etc. are some examples of vectors.
|
-
These have only positive value.
|
-
These have both positive as well as negative value.
|
-
These can’t be added or subtracted algebraically.
|
-
These can be added or subtracted algebraically.
|
13. What do you mean by distance?
-
The
length of the path travelled by a body between any two points is known as
distance. It is a scalar quantity.
14. What do you mean by displacement?
-
The
shortest distance between any two points in a particular direction is known as
displacement. It is a vector quantity.
15. Write down the differences
between distance and displacement.
-
Following
are the differences between distance and displacement:
Distance
|
Displacement
|
-
It
is the length of path joining any two points
|
-
It
is shortest distance between any two points in particular direction.
|
-
It
is the scalar quantity.
|
-
It
is the vector quantity.
|
16. Can
displacement be zero when distance is not zero?
-
Yes.
If distance is not raveled in a particular direction, then there is no
displacement.
17. Can
distance is zero when displacement is not zero?
-
No.
Because displacement is the distance traveled in the particular direction. So,
when distance is not zero when displacement is not zero.
18. Can
distance traveled by an object be smaller than magnitude of its displacement?
-
No.
Because magnitude of displacement is always less than magnitude of distance.
19. What do you mean by speed?
-
The
distance traveled by a body per unit time is known as speed. It is a scalar
quantity. Its unit is m/s. Mathematically, Speed (v) = distance traveled (d)/
time taken (t)
20. What do you mean by velocity?
-
The
distance traveled by a body per unit time in a particular direction is known
as velocity. It is a vector quantity. Its unit is m/s.
Mathematically, Velocity
(v) = displacement (s)/time taken (t)
(In another word, velocity is the displacement
of a body per unit time.)
21. What are the differences between
speed and velocity?
-
The
following are the differences between speed and velocity:
Speed
|
Velocity
|
-
It
is the distance traveled by a body per unit time.
|
-
It
is the displacement of a body per unit time.
|
-
It
is a scalar quantity.
|
-
It
is a vector quantity.
|
22. What
are the similarities between speed and velocity?
-
The
unit m/s.
23. A
body has speed of 10 m/s. What does it mean?
-
It
means that the body covers the distance of 10 m in each and every second.
24. A
body has velocity of 15 m/s. What does it mean?
-
It
means that the body covers the distance of 15 m in each and every second in a
particular direction.
25. What is average speed?
-
The
total distance traveled by a body in a certain time period is known as average
speed. Mathematically, Average Speed = Total distance traveled (d)/Total time
taken(t)
26. What is average velocity?
-
The
total displacement of a body in a certain time period is known as average
velocity. Mathematically, Average Velocity = Total displacement (s)/Total time
taken (t)
In another form, Average
Velocity = (v1 + v2)/2
Similarly, Average
Velocity = [initial velocity (u) + final velocity (v)]
/2
27. What is acceleration?
-
The
rate of change of velocity is known as acceleration. The SI unit of
acceleration is ms-2 (meter
per second square, m/s2). Similarly the negative acceleration is
known as retardation. Mathematically, Acceleration (a) = [Final velocity(v) –
Initial velocity(u)]/Total time taken(t)
28. A
body has an acceleration of 12ms-2, what does it mean?
-
It
means that the body is increasing its velocity by 12ms-1 (m/s, meter
per second) in each and every second.
29. A
body has an acceleration of 12ms-2, what does it mean?
-
It
means that the body is decreasing its velocity by 12ms-1 (m/s, meter
per second) in each and every second.
30. When
a body is thrown vertically upward, what is velocity at the highest point?
-
It
will be zero, because there the body will stop. When a moving body stops, then
its final velocity becomes zero.
31. Can
a velocity and acceleration point in opposite direction?
-
Yes,
when a body is thrown vertically upward.
32. Can
speed of a body vary with its constant velocity?
-
No,
it is not possible. (Because for constant velocity direction and distance per
unit time should be constant. For
variable speed, distance traveled per unit time and direction is not constant.)
33. What is relative motion?
-
The
motion of a body explained with respected to a reference frame is called the
relative motion.
34. What is relative velocity?
-
The
velocity of a body with respect to another moving body is called as relative
velocity.
35. How relative velocity of two
bodies is calculated?
-
The
relative velocity is calculated by two ways:
a)
Moving
in the opposite direction: the relative velocity of two bodies moving in the
opposite direction is calculated by adding velocity of both bodies.
b)
Moving
in the same direction: the relative velocity of two bodies moving in the same
direction is calculated by subtracting velocity of one from the velocity of
other bodies.
36. What
is the relative velocity of two bodies moving in the same direction with same
velocity?
-
The
relative velocity of two bodies moving in the same direction with same velocity
is zero.
37. What are equations of motions?
-
v
= u + at, s = (u+v) x t/2
, s = ut + 1/2at2, v2 = u2 + 2as are equation
of motions. These can be explained with five parameters which can be remembered
as “suvat” or “utsav”.
38. Prove v = u + at.
-
u
= initial velocity
t = time taken
s = total
displacement
a = acceleration
v = final velocity
as per definition,
acceleration = (final velocity – Initial velocity)/time taken
or, a = (v-u)/t
or, at = v – u
or, v – u = at
or, v = at + u
or, v = u + at … … … (i),
hence proved.
39. Prove s = ut + 1/2at2.
u
= initial velocity
t = time taken
s = total
displacement
a = acceleration
v = final velocity
as per definition,
acceleration = (final velocity – Initial velocity)/time taken
or, a = (v-u)/t
or, at = v – u
or, v – u = at
or, v = at + u
or, v = u + at … … … (i)
Similarly,
total displacement = average velocity x time taken
or, s = (u + v) x t/2
or, s = (u + u + at) x t/2
or, s = (2u + at) x t/2
or, s = (2ut + at2)/2
or, s = 2/2ut + at2/2
or, s = ut + 1/2at2 … …
…(ii), hence proved.
40. Prove v2 = u2
+ 2as.
u
= initial velocity
t
= time taken
s
= total displacement
a
= acceleration
v
= final velocity
as
per definition, acceleration = (final velocity – Initial velocity)/time taken
or, a = (v-u)/t
or, at = v – u
or, v – u = at
or, v = at + u
or, v = u + at … … … (i)
Squaring
on both side of equation (i), we get,
v2 = (u + at)2
or,
v2 = u2 +2uat + a2t2
or,
v2 = u2 + 2a ut + 1/2at2 2a
or,
v2 = u2 + 2a(ut + 1/2at2)
or,
v2 = u2 + 2as … … … (ii), hence proved.
41. What
is the acceleration of a person moving with uniform speed?
-
0 m/s2
42. A car having mass of 1200kg is
running with speed of 50m/s. The speed of the car reduced to 20m/s in 20s when
driver applied brake seeing a child on the path. Calculate the retardation of
the car and force applied by the driver. Also calculate the distance covered.
-
Given,
initial velocity (u) = 50m/s
final velocity (v) = 20m/s
time taken (t) = 20s
mass of the car (m) = 1200kg
acceleration (a) = ?
force (f) = ?
we know that, a =
(v-u)/t
= (20-50)/20
= -30/20
= -1.5 m/s2
Again, as per
Newton’s Second Law of Motion, F = ma
= 1200 x 1.5
=
1800N
Similarly, s = ut +
1/2at2
= 50x20 + (-1.5)x202/2
= 1000 – 300
= 700 m
Therefore, the retardation is
1.5m/s2, force applied is 1800N and distance covered is 700m
.
43. A bus is travelling with a
velocity of 90km/hr. On seeing school children 20m ahead on the road, the
driver applies the brake and the bus stops in a distance of 1.2s. What is its
retardation and mention whether the accident happens or not?
-
Given,
initial velocity (u) = 90km/hr = 90x1000/60x60 = 90000/3600 = 25m/s
final velocity (v) = 0 m/s
time taken (t) = 1.2s
retardation (a) = ?
distance covered(s) = ? (dear students, we have to calculate
distance covered by vehicle to know whether accident happens or not. If the
distance covered by vehicle is more than the distance where the driver sees the
children, i.e. 20m, accident happens, otherwise not.)
We know that, acceleration (a) =
(v-u)/t
= (0-25)/1.2
= - 2.8m/s2
Similarly, distance covered (s) =
(u+v)xt/2
=
(25+0)x1.2/2
=
(25x1.2)/2
=30/2
=15m(Accident
doesn’t happen).
44. A car starts from rest. It
maintains an acceleration of 0.5m/s2 up to 2 km. Calculate its final
velocity and time taken to cover the distance of 1.6km.
-
Given,
Initial velocity (u) = 0
Acceleration (a) = 0.5 m/s2
Distance (s) = 1.6km = 1.6x1000 =
1600m
Final velocity (v) = ?
Time taken (t) = ?
We know that, v2 = u2 + 2as
or, v = √(0+2x0.5x1600)
= 40m/s
again, t = (v-u)/a
or,
t = (40-0)/0.5 = 80s.
- GOOD LUCK -
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