The velocity and acceleration vectors of a particle undergoing circular motion are $\overrightarrow{ v }=2 \hat{ i } m / s$ and $\overrightarrow{ a }=2 \hat{ i }+4 \hat{ j } m / s ^2$ respectively at an instant of time. The radius of the circle is $........\,m$
$1$
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A particle is moving in a circle
Can you associate vectors with $(a)$ the length of a wire bent into a loop, $(b)$ a plane area, $(c)$ a sphere ? Explain.
A particle moves in a circular path of radius $R$ with an angular velocity $\omega = a -bt$ where $a$ and $b$ are positive constants and $t$ is time. The magnitude of the acceleration of the particle after time $\frac {2a}{b}$ is
A particle describes a horizontal circle of radius $r$ on the smooth surface of an inverted cone as shown. The height of plane of circle above vertex is $h$. The speed of particle should be
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 ?