A body moves with a velocity of $2\, m s ^{-1}$ for $5\, s$, then its velocity increases uniformly to $10\, m s ^{-1}$ in next $5\, s.$ Thereafter, its velocity begins to decrease at a uniform rate until it comes to rest after $5\, s$.

$(i)$ Plot a velocity-time graph for the motion of the body.

$(ii)$ From the graph, find the total distance covered by the body after $2\, s$ and $12\, s$.

A frog hops along a straight line path from point $'A^{\prime}$ to point ${ }^{\prime} B ^{\prime}$ in $10\, s$ and then turns and hops to point ${ }^{\prime} C^{\prime}$ in another $5\, s$. Calculate the average speed and average velocity of the frog for the motion between $(a)(A)$ to $(B)(b)(A)$ to $(C)($ through $B)$

Write true or false for the following statements

Acceleration is defined as the rate of change of velocity.

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

State the type of motion represented by the given graph.