If the instantaneous velocity of a particle projected as shown in figure is given by $v =a \hat{ i }+(b-c t) \hat{ j }$, where $a, b$, and $c$ are positive constants, the range on the horizontal plane will be

A particle does uniform circular motion in a horizontal plane. The radius of the circle is $20$ cm. The centripetal force acting on the particle is $10\, N$. It's kinetic energy is ........ $J$

A particle is moving eastwards with velocity of $5\,m/s$. In $10 \,sec$ the velocity changes to $5 \,m/s$ northwards. The average acceleration in this time is

A particle is projected with a velocity $v$ such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is (where $g$ is acceleration due to gravity)

A particle is projected from a horizontal plane such that its velocity vector at time $t$ is given by $\vec v = a\hat i + (b - ct)\hat j$ . Its range on the horizontal plane is given by

The $x-t$ graph of a particle moving along a straight line is shown in figure The $a-t$ graph of the particle is correctly shown by