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.
Draw the distance$-$time graph for the following situations
$(a)$ When a body is stationary.
$(b)$ When a body is moving with a uniform speed.
$(c)$ When a body is moving with non$-$uniform speed.
Area under velocity$-$time graph is equal to the
A train starting from rest picks up a speed of $10\, m s ^{-1}$ in $100\, s$. It continues to move at the same speed for the next $250\, s$. It is then brought to rest in the nert $50\, s$. Plot a speed$-$time graph for the entire motion of the train.
$(i)$ acceleration of the train while accelerating,
$(ii)$ retardation of the train while retarding,
$(iii)$ and the total distance covered by the train.
When is the acceleration $(i)$ positive $(ii)$ negative ?
Write true or false for the following statements
A body is said to be at rest, if it does not change its position with respect to the reference point.