$A$ particle moves around a circular path of radius $r$ with uniform speed $V$. After moving half the circle,the average acceleration of the particle is

State whether the following statements are true or false:
$(a)$ If the angular velocity is constant on a circular path,the linear velocity is also constant.
$(b)$ In projectile motion,the velocity vector of the projectile is always perpendicular to the acceleration vector.
$(c)$ For the maximum horizontal range $R$ of a projectile,the maximum height attained is $\frac{R}{4}$.
$(d)$ If $|\vec{A} \times \vec{B}| = AB$,then the angle between $\vec{A}$ and $\vec{B}$ is zero.

$A$ particle starts from the origin at $t=0$ with an initial velocity of $3.0 \hat{i} \; m/s$ and moves in the $x-y$ plane with a constant acceleration $(6.0 \hat{i} + 4.0 \hat{j}) \; m/s^2$. The $x$-coordinate of the particle at the instant when its $y$-coordinate is $32 \; m$ is $D$ meters. The value of $D$ is

The figure shows the velocity and the acceleration of a point-like body at the initial moment of its motion. The direction and the absolute value of the acceleration remain constant. Find the time when the speed becomes minimum. (Given: $a = 4\, m/s^2$,$v_0 = 40\, m/s$,$\phi = 143^o$)

$A$ car travels north with a uniform velocity. It goes over a piece of mud which sticks to the tyre. The particles of the mud,as they leave the ground,are thrown:

What is the value of linear velocity,if $\vec \omega = 3\hat i - 4\hat j + \hat k$ and $\vec r = 5\hat i - 6\hat j + 6\hat k$?