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 has initial velocity $(3\hat i + 4\hat j$$ ) $ and has acceleration $(0.4\,\hat i + 0.3\,\hat j)$ . Its speed after $10\,s$ is

A projectile is given an initial velocity of $(\hat i+2\hat j)\,m/ s$ where $\hat i$ is along the ground and $\hat j$ is along the vertical. If $g = 10\,m/s^2,$ the equation of its trajectory is

In projectile motion, the modulus of rate of change of velocity

A point $P$ moves in counter clock wise direction on a circular path as shown in figure.  The movement of $'P'$ is such that it sweeps out a length $S = t^3 + 5$, where $'S'$ is in meter and $t$ is in seconds. The radius of the path is $20\, m$. The acceleration of $'P'$ when $t = 2\, sec$. is nearly     ......... $m/s^2$

A body of mass $1 \,kg$ is projected from ground at an angle $30^{\circ}$ with horizontal on a level ground at a speed $50 \,m / s$. The magnitude of change in momentum of the body during its flight is ....... $kg ms ^{-1}$ $\left(g=10 \,m / s ^2\right)$