A missile is fired for maximum range at your town from a place $100\, km$ away from you. If the missile is first detected at its half way point, how much warning time will you have ? (Take $g = 10\, m/s^2$) what was the speed of missile when it was detected ?

A particle moves with constant angular velocity in circular path of certain radius and is acted upon by a certain centripetal force $F$. If the angular velocity is doubled, keeping radius the same, the new force will be

A car goes around 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 $2 R$ and experiences a centripetal acceleration of magnitude $8 a_c$. Then, its time period is

A stone tied to the end of a string of $1\, m$ long is whirled in a horizontal circle with a constant speed. If the stone makes $22$ revolution in $44\, seconds$, what is the magnitude and direction of acceleration of the stone?

A horizontal curve on $a$ racing track is banked at a $45^o $ angle. When a vehicle goes around this curve at the curve’s safe speed (no friction needed to stay on the track), what is its centripetal acceleration?

An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at $x =+2\,m$, its velocity is $-4 \hat{ j }\, m / s$. The object's velocity $(v)$ and acceleration $(a)$ at $x =-2\,m$ will be