Give one example for each of the type of motion when

$(i)$ acceleration is in the direction of motion.

$(ii)$ acceleration is against the direction of motion.

$(iii)$ acceleration is uniform.

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$(i)$ The motion of a car when it starts from rest and increases its velocity at a constant rate in a particular interval of time.

$(ii)$ The motion of a train when it slows down on approaching a station.

$(iii)$ The motion of a ball falling down freely.

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Distance$-$time graph below represents the motion of two buses $A$ and $B$

$(i)$ What is the distance by which bus $B$ was ahead of bus $A$ initially ?

$(ii)$ Do they ever meet each other ? If so, when ?

$(iii)$ What is the distance travelled by bus $A$ when it overtakes bus $B$ ?

$(iv)$ Find out the distance by which bus $A$ was ahead of bus $B$ at $y=12 h$

$(v)$ Which one of them is moving faster ? Give reason.

Why does (second)$^{2}$ occur in the unit of acceleration ?

An aeroplane lands at $216\, km\, h ^{-1}$ and stops after covering a runway of $2\, km .$ Calculate the acceleration and the time, in which its comes to rest.

$(a)$ Draw velocity-time graph for the following cases

$(i)$ When the object is at rest.

$(ii)$ When the object is thrown vertically upwards.

$(b)$ A motorcyclist riding motorcycle $A$ who is travelling at $36\, km h^{-1}$ applies the brakes and stops the motorcycle in $10\, s$. Another motorcyclist of motorcycle $B$ who is travelling at $18\, km h^{-1}$ applies the brakes and stops themotorcycle in $20\, s$. Plot speed-time graph for the two motorcycles. Which of the two motorcycles travelled farther before it come to a stop ?

The driver of a train $A$ travelling at a speed of $54\, km h^{-1}$ applies brakes and retards the train uniformly The train stops in $5\, s$. Another train $B$ is travelling on the parallel track with a speed of $36\, km h ^{-1}$. This driver also applies the brakes and the train retards uniformly. The train $B$ stops in $10\, s$. Plot speed time graph for both the trains on the same paper. Also, calculate the distance travelled by each train after the brakes were applied.