A particle crossing the origin at time $t=0$ moves in the $X Y$-plane with a constant acceleration ' $a$ ' in $y$-direction. If the equation of motion of the particle is $y=b x^2$ (where $b$ is a constant), then its velocity component in the $x$-direction is

If a ball projected vertically upwards with certain initial velocity from the ground crosses a point at a height of 25 m twice in a time interval of 4 s , then the initial velocity of the ball is

(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A car is moving with a velocity of $4 \mathrm{~ms}^{-1}$ towards east. After a time of 4 s , if it is heading north-east with a velocity of $4 \sqrt{2} \mathrm{~ms}^{-1}$, then the average velocity of the car is

A body of mass 5 kg starts from the origin with an initial velocity $(30 \hat{\mathbf{i}}+40 \hat{\mathbf{j}}) \mathrm{ms}^{-1}$. If a constant force $-(\hat{\mathbf{i}}+5 \hat{\mathbf{j}}) \mathrm{N}$ acts on the body, then the time in which the $y$-component of its velocity becomes zero is