What is the relation between distance and time

$(i)$ when body is moving with uniform velocity ?

$(ii)$ when body is moving with variable velocity ?

Following figure is the speed-time graph for a rocket from the moment when the fuel starts to burn, i.e. at time $t=0$.

$(a)$ State the acceleration of the rocket at $t=0$.

$(b)$ State what happens to the acceleration of the rocket between $t=5 s$ and $t=60 s$.

$(c)$ Calculate the acceleration of rocket at $t=80 s$ Give reason for your answer.

$(d)$ The total mass of the rocket at $t=80\, s$ is $1.6 \times 10^{6}\, kg .$ Calculate the resultant force on the rocket at this time. Give reason for your answer.

A particle accelerates from rest at a constant rate for sometime and attains a constant velocity of $8\, m s ^{-1}$. Afterwards it decelerates with a constant rate and comes to rest. If the total time taken is $4$ second, the distance travelled is

All buses and cars these days are fitted with a speedometer, which shows the velocity of the vehicle. A device called odometer records the distance moved by the vehicle. If the reading on the odometer of a vehicle in the beginning of a trip and after $40$ minutes were $1048\, km$ and $1096\, km$ respectively, calculate its average velocity. Will the reading on the speedometer show this velocity when the vehicle is moving ? Support your answer with reason.

A car starts from rest and moves along the $x-$ axis with constant acceleration $5\, ms^{-2}$ for $8\,\sec $. If it then continues with constant velocity, what distance will the car cover in $12\,\sec $ since it started from the rest ?