A ball is dropped from a tower. In the last second of its motion, it travels a distance of $15 \mathrm{m}$. Find the height of the tower. [Take$\left.g=10 \mathrm{m} {\sec }^{-2}\right]$

A toy plane $P$ starts flying from point $A$ along a straight horizontal line $20 \mathrm{m}$ above ground level starting with zero initial velocity and acceleration $2 \mathrm{m} {\mathrm{s}}^{-2}$ as shown. At the same instant, a man $P$ throws a ball vertically upwards with an initial velocity $u$. Ball touches (coming to rest) the base of the plane at point $B$ of the plane's journey when it is vertically above the man. $S$ is the distance of point $B$ from point $A$. Just after the contact of the ball with the plane, the acceleration of the plane increases to $4 \mathrm{m} {\mathrm{s}}^{-2}$. Find,

(i) The initial velocity $u$ of the ball.
(ii) Distance $S$.
(iii) Distance between man and plane when the man catches the ball back. $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$ (Neglect the height of a man.)

For a particle moving along $x$-axis, the velocity-time graph is as shown in the figure. Find the distance travelled and displacement of the particle. Also, find the average velocity of the particle in interval $0$ to $5 \mathrm{s}$.

A cart started at $t=0,$ its acceleration varies with time as shown in the figure. Find the distance travelled in $30$ seconds and draw the position-time graph.

Two particles $A$ and $B$ start from rest and move for equal time on a straight line. The particle $A$ has an acceleration $a$ for the first half of the total time and $2a$ for the second half. The particle $B$ has an acceleration $2a$ for the first half and $a$ for the second half. Which particle has covered a larger distance?