$A$ car moving with a linear speed of $72 \ km/h$ has wheels of radius $0.250 \ m$. If the wheels come to rest after $20$ rotations upon applying brakes,the angular retardation produced by the brakes is ....... $rad \ s^{-2}$. (in $.5$)

Two bodies are projected from the ground with the same speed $40 \ m/s$ at two different angles with respect to the horizontal. The bodies were found to have the same range. If one of the bodies was projected at an angle of $60^{\circ}$ with the horizontal,then the sum of the maximum heights attained by the two projectiles is $....... \ m$. (Given $g = 10 \ m/s^2$)

If $\alpha$ is angular acceleration,$\omega$ is angular velocity,and $a$ is the centripetal acceleration,then which of the following is true?

$A$ truck starts from rest and accelerates uniformly at $2.0 \; m s^{-2}$. At $t = 10 \; s$,a stone is dropped by a person standing on the top of the truck ($6 \; m$ high from the ground). What are the $(a)$ velocity,and $(b)$ acceleration of the stone at $t = 11 \; s$? (Neglect air resistance.)

$A$ particle has initial velocity $(2\hat{i} + 3\hat{j})$ and acceleration $(0.3\hat{i} + 0.2\hat{j})$. The magnitude of velocity after $10\, s$ will be:

In the projectile motion of an object,the object reaches its maximum height where its speed is half of its initial speed. Then the ratio between the range and the maximum height of the projectile is