Explain with reason, which of the following graphs can possibly represent the motion of a particle observed in nature ?

$(a)$ This graph shows that with increase in time distance first increases and then decreases.

However, distance can never decrease with time, so this graph is not possible.

$(b)$ This graph shows that at a certain time $t_{1}$ ' the body is present at two positions. It also shows that first time increases and then decreases. Since both these conditions cannot be realised in practice, hence, this graph is not possible.

$(c)$ This graph shows that speed is negative for some interval of time. Since speed cannot be negative, this graph is also not possible.

$(d)$ This graph shows that at a given instant of time the particle has two velocities. Also, it shows that at some time it. has infinite acceleration (graph parallel to the velocity axis) : Both these conditions cannot be achieved in practice, therefore, this graph is also not possible.