$A$ projectile is thrown in the upward direction making an angle of $60^{\circ}$ with the horizontal with a velocity of $140 \,ms^{-1}$. Then the time after which its velocity makes an angle $45^{\circ}$ with the horizontal is (Acceleration due to gravity, $g=10 \,ms^{-2}$) (in $\,s$)

$A$ car goes around a uniform circular track of radius $R$ at a uniform speed $v$ once in every $T$ seconds. The magnitude of the centripetal acceleration is $a_c$. If the car now goes uniformly around a larger circular track of radius $2R$ and experiences a centripetal acceleration of magnitude $8a_c$,then its time period is:

$A$ car is moving with a velocity of $4 \,m \,s^{-1}$ towards east. After a time of $4 \,s$, if it is heading north-east with a velocity of $4 \sqrt{2} \,m \,s^{-1}$, then the average velocity of the car is

If a body of mass $2 \,kg$ moving with an initial velocity of $4 \,m \,s^{-1}$ is subjected to a force of $3 \,N$ for a time of $2 \,s$ normal to the direction of its initial velocity, then the resultant velocity of the body is

If a body moving in a circular path maintains a constant speed of $10\,ms^{-1},$ then which of the following correctly describes the relation between acceleration and radius?

As shown in the figure,there is a spring-block system. $A$ block of mass $500\,g$ is pressed against a horizontal spring fixed at one end to compress the spring by $5.0\,cm$. The spring constant is $500\,N/m$. When released,calculate the horizontal distance from the edge of the table where it will hit the ground $4\,m$ below the spring. $(g = 10\,m/s^2)$