During which time interval is the particle described by these position graphs at rest?

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

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

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

Two seconds after projection a projectile is travelling in a direction inclined at $30^o$ to horizontal, after one more second it is travelling horizontally. What is the magnitude and direction of its velocity at initial point