An athlete completes one round of a circular track of radius $10 \, m$ in $40 \, sec$. The distance covered by him in $2 \, min \ 20 \, sec$ is ........ $m$.

$A$ particle of mass $m$ moves with constant speed $v$ on a circular path of radius $r$ as shown in the figure. The average force on it during its motion from $A$ to $B$ is

$A$ particle is moving with velocity $\vec v = K(y\hat i + x\hat j)$ where $K$ is a constant. The general equation for its path is

$A$ particle is projected with velocity $u$ from point $M$ on a frictionless incline of length $20\sqrt{2} \, m$. If it crosses a $40 \, m$ wide well at an angle of $45^o$,what should be its velocity at point $M$?

$A$ car moving with a certain velocity jumps from an inclined plane placed at one bank of a river and reaches the other bank by attaining a maximum height of $80 \,m$. If the same car, moving with the same velocity, jumps from another inclined plane having a different angle of inclination and reaches the same point on the other bank by attaining a maximum height of $45 \,m$, then the width of the river is: (in $\,m$)

Three particles,located initially on the vertices of an equilateral triangle of side $L$,start moving with a constant speed $v$ towards each other in a cyclic manner,forming spiral loci that converge at the centroid of the triangle. The length of one such spiral locus will be