What is the numerical ratio of average velocity to average speed of an object when it is moving along a straight path ?

The $v-t$ graph of cars $A$ and $B$ which start from the same place and move along straight road in the same direction, is shown. Calculate

$(i)$ the acceleration of car $A$ between $0$ and $8\, s$.

$(ii)$ the acceleration of car $B$ between $2\, s$ and $4\, s$.

$(iii)$ the points of time at which both the cars have the same velocity.

$(iv)$ which of the two cars is ahead after $8\, s$ and by how much ?

Define 'average speed'. An object moves with a uniform speed of $10\, m s ^{-1}$ for $5 s$ and then with a uniform speed of $5\, m s ^{-1}$ for $10\, s$. Find its average speed.

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 ?

Two cars moving in opposite directions cover same distance $'d'$ in one hour. If the cars were moving in north$-$south direction, what will be their displacement in one hour ?

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.