A boat crosses a river from part $A$ to part $B$, which are just on the opposite side. The speed of the water. $v_\omega$ and the of boat is $v_B$ relative to still water. Assume $v_B=\sqrt{2} v_\omega$. What is the time taken by the boat, if it has to cross the river directly on the $A B$ line ($D=$ width of the river) ?

A projectile is projected with the velocity of $(3\widehat i + 4\widehat j)$ m/s. The horizontal range of the projectile will be

A man walks in a straight line for 5 min with a velocity of 45 m/s. What is the speed with which he has to move in order to comeback to its original position in 1.5 min?

A projectile is given an initial velocity of $(\widehat i + \widehat j)$ m/s, where, $\widehat i$ is along the ground and $\widehat j$ is along the vertical. If g = 10 m/s², then the equation of its trajectory is

Based on the provided velocity-time graph for an object’s straight-line movement, determine the total distance covered and the average speed between t = 0 and t = 20 seconds.

The acceleration of a particle in m/s² is given by a = (3t² $-$ 2t + 1), where t is in second. If the particle starts with a velocity v = 1 m/s at t = 1s, then velocity of the particle at the end of 4s is