(a) Rest and motion are relative terms/
(b) Yes. An object may be at rest relative to one object and at the same time it may be in motion relative to another object.
(c) Moving.

SI unit of speed is meter per second. The average speed of the body is given by
\({ v }_{ av }\quad =\frac { { v }_{ 1 }{ t }_{ 1 }+{ v }_{ 2 }{ t }_{ 2 } }{ { t }_{ 1 }+{ t }_{ 2 } } \)
Here, \({ v }_{ 1 }\)= 6 km/h, \({ t }_{ 1 }\)=2 h,\({ v }_{ 2 }\) = 4 km/h,\({ t }_{ 2 }\) = 3 h
\({ v }_{ av }\)       = \(\frac { 6\times 2+4\times 3 }{ 2+3 } \)= 4.8 km/h
\(\therefore \)Total distance = \({ v }_{ 1 }{ t }_{ 1 }+{ v }_{ 2 }{ t }_{ 2 }\) = \(6\times 2+4\times 3\) = 24km

Here u = 90 km/h = 90 x \(\frac { 5 }{ 18 } ms^{ -1 }=25ms^{ -1 }\)
a =-.0.5 m \(s^{ -2 }\),v = 0
As \(v^{ 2 }-u^{ 2 }=2as\)
\(\therefore 0^{ 2 }-25^{ 2 }=2X(-0.5)Xs\)
or \(s=\frac { 25x25 }{ 2x0.5 } \)  = 625 m.

(i) The body is moving with uniform velocity.
(ii) The body is moving with uniform velocity.

(i) Uniform velocity: If a body covers equal distances in equal intervals of time, however small these intervals may be in a given direction, its velocity is said to be 'uniform velocity' So in uniform velocity a body moves with uniform speed in a given direction, for example, light travels with a uniform velocity of 3-10 m/s through the vacuum.
(ii) Variable velocity When a body travels unequal distances intervals of time or its direction changes or both change its velocity is said to be 'variable velocity' for example a bus turning at a junction has variable velocity.

Velocity. It is a physical quantity that gives both the speed and direction of motion of the body
Velocity of a body is defined as the displacement produced per unit of time. It is also defined as the speed of a body in a given direction.
Velocity = \(\frac { Displacement }{ Time } \)
If s is the distance traveled by a body in a given direction and t is the time taken to travel that distance, then the velocity v is given by
\(v=\frac { s }{ t } \)
The SI unit of velocity is \(ms^{ -1 }\).

An object may be at rest relative to one surrounding object and at the same time it may be in motion relative to some other object For example a passanger sitting in a  moving train is at rest relative to other passengers of his compartment.But since he is sharing the motion of the train.so he is in motion relative to the outside trees, lamp posts railway stations etc Thus,rest and motion are relative terms.

Rest .A body is said to be at rest if it does not change its position with respect to its surroundings.A table lying in a room is at rest with respect to the walls of the room.
Motion .A body is said to be in motion if it changes its position with respect to its surroundings Thus , motion means movement of bodies A car running on the road is in motion with respect to the lamp posts,trees or bus stop on the roadside.

(a) Speed is defined as the distance travelled by a body per unit time.
(b) The SI unit of speed is m s^-1
(c) Average speed is the total distance travelled by a body, divided by the total time taken to cover that distance.
(d) No, the average speed of an object can't be negative.

Here u = 5 \(ms^{ -1 }\)
As the acceleration acts in the opposite direction of initial velocity so it is negative
a = -10 \(ms^{ -1 }\)
At the highest point v = 0
Using \(v^{ 2 }-u^{ 2 }=2as,\) we get
\(0^{ 2 }-5^{ 2 }=2x(-10)xs\)
\(s=\frac { 25 }{ 20 } =1.25m\)
Height attained by the stone = 1.25 m
Again v = u + at
0 = 5-10 x t
t = \(\frac { 5 }{ 10 } \) = 0.5s
Time is taken by the stone to reach the highest point = 0.5s

Different types of Motions:
1.Translatory Motion When a body moves as a whole along a straight or curved path, it is said to be in translatory motion.It is again of two types:
(i) Rectilinear motion Here a body moves as a whole along a straight path.For example a train moving on straight rails has translatory rectilinear motion.
(ii) Curvilinear motion.Here a body moves as a whole along a curved path For example motion of a bicycle taking a turn along a curved path.
2.Rotatory motion.When a body rotates about a fixed point or axis , it has rotatory motion For example motion of a flywheel about a shaft.
3.Vibratory or oscillatory motion. When a body moves to and from about a mean position again and again it has vibratory or oscillatory motion For example the motion of the pendulum of a wall clock. 
4.Complex motion. Sometimes ,the motion of a body may be a combination of more than one types of motion For example a ball rolling down an inclined plane has botth translatoruy and rotatory motions.

a = 8 \(ms^{ -2 }\),v = 32 \(ms^{ -1 }\) 
(ii) t = \(2\sqrt { 2\quad s } \)