$A$ stone is thrown in a vertically upward direction with a velocity of $5 \, m s^{-1}$. If the acceleration of the stone during its motion is $10 \, m s^{-2}$ in the downward direction,what will be the height attained by the stone and how much time will it take to reach there?

$A$ farmer moves along the boundary of a square field of side $10 \, m$ in $40 \, s$. What will be the magnitude of displacement (in $m$) of the farmer at the end of $2 \, min \; 20 \, s$ from his initial position?

Joseph jogs from one end $A$ to the other end $B$ of a straight $300 \, m$ road in $2 \, min$ $30 \, sec$ and then turns around and jogs $100 \, m$ back to point $C$ in another $1 \, min$. What are Joseph's average speeds and velocities in jogging from $A$ to $C$?

The speed-time graph for a car is shown in the figure.
$(a)$ Find how far the car travels in the first $4 \, s$. Shade the area on the graph that represents the distance travelled by the car during this period.
$(b)$ Which part of the graph represents the uniform motion of the car?

State which of the following situations are possible and give an example for each of these:
$(a)$ An object with a constant acceleration but with zero velocity.
$(b)$ An object moving with an acceleration but with uniform speed.
$(c)$ An object moving in a certain direction with an acceleration in the perpendicular direction.

$A$ driver of a car travelling at $52\, km\, h^{-1}$ applies the brakes and accelerates uniformly in the opposite direction. The car stops in $5\, s$. Another driver going at $3\, km\, h^{-1}$ in another car applies his brakes slowly and stops in $10\, s$. On the same graph paper,plot the speed versus time graphs for the two cars. Which of the two cars travelled farther after the brakes were applied?