Why we cannot use an equation of motion in case of acceleration varies with time?

A ball moving on a table reaches the edge and falls. Sketch the path it will follow while falling. 

A circular track has a circumference of $\mathrm{s} \mathrm{m}$ with AB as one of its diameter. A scooterist moves from A to B along a circular path with a uniform speed of $\mathrm{v}$ $\mathrm{m}/\mathrm{s}$. Find the distance covered by scooterist?

A circular track has a circumference of $\mathrm{s} \mathrm{m}$ with AB as one of its diameter. A scooterist moves from A to B along a circular path with a uniform speed of $\mathrm{v}$ $\mathrm{m}/\mathrm{s}$. Find the expression for the displacement of the scooterist?

A circular track has a circumference of $s \mathrm{m}$ with AB as one of its diameter. A scooterist moves from A to B along a circular path with a uniform speed of $v$ $\mathrm{m}/\mathrm{s}$. Find the expression for time taken by the scooterist in moving from A to B?

The graph given below is the distance-time graph of an object. Find expression for the speed of the object during the first $t_1$ second of its stationary position. 

 

The graph given below is the distance-time graph of an object.

The graph given below is the distance-time graph of an object.

Does it represent a real situation? Justify your answer.