Motion · Physics · VITEEE

The velocity of a particle moving in a straight line varies with time in such a manner that $v$ versus $t$ graph is velocity is $v_m$ and the total time of motion is $t_0$

(i) Average velocity of the particle is $\frac{\pi}{4} v_m$

(ii) Such motion cannot be realized in practical terms

Choose the correct option on the basis of above two statements.

The height $y$ and the distance $x$ along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by $y=8 t-5 t^2 \mathrm{~m}$ and $x=6 t \mathrm{~m}$, where $t$ is in seconds. The velocity with which the projectile is projected is

A ball is projected horizontally with a velocity of $5 \mathrm{~ms}^{-1}$ from the top of a building 19.6 m high. How long will the ball take to hit the ground?

The horizontal range of a projectile is $4 \sqrt{3}$ times of its maximum height. The angle of projection will be

The position of a projectile launched from the origin at $$t=0$$ is given $$\mathbf{r}=(40 \hat{\mathbf{i}}+50 \hat{\mathbf{j}}) \mathrm{m}$$ at $$t=2 \mathrm{~s}$$. If the projectile was launded at an angle $$\theta$$ from the horizontal, then $$\theta$$ is (take, $$g=10 \mathrm{~m} / \mathrm{s}^2$$ )