There are $5$ houses on a street,$A, B, C, D$ and $E$. For all cases,assume that positions to the right are positive.
$(i)$ Draw a frame of reference with house $A$ as the origin and the positions of houses $B, C, D$ and $E$.
$(ii)$ You live in house $C$. What is your position relative to house $E$?
$(iii)$ What are the positions of houses $A$ and $D$,if house $B$ is taken as the reference point?

An electron moving with a velocity of $5 \times 10^{4} \, ms^{-1}$ enters into a uniform electric field and acquires a uniform acceleration of $10^{4} \, ms^{-2}$ in the direction of its initial motion.
$(i)$ Calculate the time in which the electron would acquire a velocity double of its initial velocity.
$(ii)$ How much distance the electron would cover in this time?

Account for the following:
$(a)$ Name the quantity which is measured by the area occupied below the velocity$-$time graph.
$(b)$ Give an example of an object moving in a certain direction with acceleration in the perpendicular direction.
$(c)$ Under what condition is the magnitude of average velocity of an object equal to its average speed?
$(d)$ Give an example of uniformly accelerated motion.
$(e)$ $A$ body is moving along a circular path of radius $r$. What will be the distance and displacement of the body when it completes half a revolution?

The branch of Physics which deals with the motion of objects while taking into consideration the cause of motion is

An object starts a linear motion with velocity $u$ and with uniform acceleration $a$,it acquires a velocity $v$ in time $t$.
$(a)$ Draw its velocity-time graph.
$(b)$ Obtain the first equation of motion,$v = u + at$,for the velocity-time relation by using the velocity-time graph.
$(c)$ $A$ body moving with a velocity of $2 \, m s^{-1}$ acquires a velocity of $10 \, m s^{-1}$ in $5 \, s$. Find its acceleration.

$A$ body moves with a velocity of $2\, m s^{-1}$ for $5\, s$,then its velocity increases uniformly to $10\, m s^{-1}$ in the next $5\, s$. Thereafter,its velocity begins to decrease at a uniform rate until it comes to rest after $5\, s$.
$(i)$ Plot a velocity-time graph for the motion of the body.
$(ii)$ From the graph,find the total distance covered by the body after $2\, s$ and $12\, s$.