If the displacement of an object is proportional to square of time, then the object moves with

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

$(a)$ Which type of motion is represented by the velocity$-$time graph shown below ?

$(b)$ Name the physical quantity which can be calculated by the area of rectangle $OABC$.

$(c)$ What does the straight line $AB$ represents ?

An object is dropped from rest at a height of $150\, m$ and simultaneously another object is dropped from rest at a height $100 \,m$. What is the difference in their heights after $2\,\sec $ if both the objects drop with same accelerations ? How does the difference in heights vary with time ?

If the displacement$-$time graph for a particle is parallel to time axis, what is the velocity of the particle ?

$(a)$ Derive graphically the equation for velocity$-$time relation.

$(b)$ Name the device used to measure distance travelled by a vehicle.

$(c)$ Can displacement of a moving object be zero ? Give reason.