The velocity-time graph of cars $A$ and $B$ which start from the same place and move along a straight road in the same direction is shown below

Calculate :

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

$(b)$ the time at which both the cars have the same velocity.

$(c)$ the distance travelled by the two cars $A$ and $B$ in $8\, s$

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

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.

A girl of mass $50\, kg$ jumps out of a moving boat of mass $300\, kg$ on to the bank with a horizontal velocity of $3\, m s ^{-1}$. With, what velocity, does the boat begin to move backwards ?

An object starting from rest travels $20\, m$ in first $2\,\sec $ and $160\, m$ in next $4\,\sec $. What will be the velocity after $7\,\sec $ from the start ?

If the displacement of a body is proportional to the square of the time elapsed, what type of motion does the body possess ?