The $x-t$ graph of a particle moving along a straight line is shown in figure The speed-time graph of the particle is correctly shown by

The equation of motion of a projectile is $y = Ax -Bx^2$ where $A$ and $B$ are the constants of motion. The horizontal range of the projectile is

A very broad elevator is going up vertically with a constant acceleration of $2\,m / s ^2$. At the instant when its velocity is $4\,m / s$ a ball is projected from the floor of the lift with a speed of $4\,m / s$ relative to the floor at an elevation of $30^{\circ}$. The time taken by the ball to return the floor is $..............\,s$ $\left(g=10\,m / s ^2\right)$

For a given angle of the projectile if the initial velocity is doubled the range of the projectile becomes

The equation of motion of a projectile is $y=12 x-\frac{3}{4} x^2$ $..........\,m$ is the range of the projectile.

For angles of projection of a projectile at angle $(45^o  +\theta)$ and $(45^o  -\theta ) $ , the horizontal range described by the projectile are in the ratio of