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

The uses of a velocity-time graph are as follows:
(i) To determine the speed of a body at any instant of time
(ii) To determine the acceleration of a body 
(iii) To detemine the total distance travelled by a body in a given time-intrerval.

Here , a = 10 \(m/s^{ 2 }\) u = 0,t = 5s,s = ?
s = \(ut+\frac { 1 }{ 2 } at^{ 2 }=0+\frac { 1 }{ 2 } X10X5^{ 2 }=125m\)
\(\therefore \) distance travelled by the object = 125 m.

Initial speed,u = 0
Final speed,v = \(40\frac { km }{ h } =\frac { 40X1000m }{ 3600s } =\frac { 100 }{ 9 } ms^{ -1 }\)
Time,t = 10 min = 600 s
Acceleration,a = \(\frac { v-u }{ t } =\frac { \frac { 100 }{ 9 } -0 }{ 600 } =\frac { 100 }{ 9X600 } ms^{ -2 }\)
\(=\frac { 1 }{ 54 } ms^{ -2 }\) 

The relationship between u, v, a, and t is a body falling freely towards the earth has a uniform acceleration of 9.8 \(m/s^{ 2 }\).

Retardation. When the velocity of a body decreases, its acceleration is negative Negative acceleration is called 'retardation' or 'deceleration' When a stone is thrown upwards, it is under retardation. Similarly, when a bus approaches a bus stop, its motion gets retarded.

Here t = 5 minutes = 300 s,v= 3 x \(10^{ 8 }ms^{ -1 }\) 
Distance of spaceship s = vt = 3 x \(10^{ 8 }\) x 300 = 9 x \(10^{ 10 }\) m.

Average speed = \(\frac { Total\quad path\quad length }{ Time\quad interval } \)
Average velocity = \(\frac { Displacement }{ Time\quad interval } \)
When an object moves along a straight line in the same direction its local path length is equal to the magnitude of displacement Hence, its average speed is equal to the magnitude of average velocity.

Differences between speed and velocity

Average velocity. When the velocity of a body changes at a non-uniform rate, its average velocity is defined as the net displacement covered divided by the total time taken.
Average velocity = \(\frac { Net\quad displacement }{ Total\quad time\quad taken } \)
When the velocity of a body changes at a uniform rate, then the average velocity is given by the arithmetic mean of initial velocity and final velocity for a given period of time.
Average velocity = \(\frac { Intial\quad velocity+Final\quad velocity }{ 2 } \)
If u is the initial velocity and v is the final velocity then the average velocity \(v_{ av }=\frac { u+v }{ 2 } \).

(i) The total distance travelled = h + h = 2h.
(ii) The displacement is zero because the initial and final positions coincide.

Distance covered after 2 complete rounds
= 2 x Circumference
= 2x 2\(\pi \) (2R) = 8 \(\pi \)R
After 2 complete rounds, the body comes back to its initial position
\(\therefore \) Displacement = 0.

(i) Motion of vehicles moving on a road can be easily and directly perceived.
(ii) we perceive the motion of air indirectly by observing the movement of dust, leaves and branches of trees.

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.