Define acceleration. State a relationship connecting $u, v, a$ and $t$ for an accelerated motion. Give an example of a motion in which acceleration is uniform.

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It is defined as the rate of change of velocity. The relation is $v=u+a t .$ Freely falling body.

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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.

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What does the slope of velocity$-$time graph represent ?

A train starting from rest picks up a speed of $10\, m s ^{-1}$ in $100\, s$. It continues to move at the same speed for the next $250\, s$. It is then brought to rest in the nert $50\, s$. Plot a speed$-$time graph for the entire motion of the train.

$(i)$ acceleration of the train while accelerating,

$(ii)$ retardation of the train while retarding,

$(iii)$ and the total distance covered by the train.

A cyclist travels a distance of $4\, km$ from $P$ to $Q$ and then moves a distance of $3\, km$ right angle to $PQ$. Find his resultant displacement graphically.