The equation of a projectile is $y=a x-b x^2$. Its horizontal range is ......

A particle moves along a straight line in such a way that it’s acceleration is increasing at the rate of $2 m/s^3$. It’s initial acceleration and velocity were $0,$ the distance covered by it in $t = 3$ second is  ........ $m$

and direction of the vectors $\hat{ i }+\hat{ j }$, and $\hat{ i }-\hat{ j }$ ? What are the components of a vector $A =2 \hat{ i }+3 \hat{ j }$ along the directions of $\hat{ i }+\hat{ j }$ and $\hat{ i }-\hat{ j } ?$

Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity $v$ and other with a uniform acceleration $a.$ If $\alpha$ is the angle between the lines of motion of two particles then the least value of relative velocity will be at time given by

Velocity-time graph for a car is semicircle as shown here. Which of the following is correct :

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