A particle starts from the origin at t=0 and moves in the x-y plane with constant acceleration 'a' in the y direction. Its equation of motion is $y=b{x}^2$. The x component of its velocity (at t=0) is:

(1) variable

(2) $\sqrt{\frac{2a}{b}}$

(3) $\frac{a}{2b}$

(4) $\sqrt{\frac{a}{2b}}$

A body is projected with a velocity \(u\) with an angle of projection \(\theta.\) The change in velocity after the time \((t)\) from the time of projection will be:

What determines the nature of the path followed by the particle?

(1) Speed only

(2) Velocity only

(3) Acceleration only

(4) None of these

A boat is sent across a river in perpendicular direction with a velocity of 8 km/hr. If the resultant velocity of boat is 10 km/hr, then velocity of the river is : 

(1) 10 km/hr

(2) 8 km/hr

(3) 6 km/hr

(4) 4 km/hr

A boat is moving with velocity of $3\hat{i}+4\hat{j}$ in river and water is moving with a velocity of $-3\hat{i}-4\hat{j}$ with respect to ground. Relative velocity of boat with respect to water is: 

(1) $-6\hat{i}-8\hat{j}$

(2) $6\hat{i}+8\hat{j}$

(3) $8\hat{j}$

(4) $6\hat{i}$

A boat moves with a speed of 5 km/h relative to water in a river flowing with a speed of 3 km/h and having a width of 1 km. The minimum time taken around a round trip(returning to the initial point) is:

(1) 5 min

(2) 60 min

(3) 20 min

(4) 30 min

A river is flowing from W to E with a speed of 5 m/min. A man can swim in still water with a velocity 10 m/min. In which direction should the man swim so as to take the shortest possible path to go to the south. 

(1) 30° with downstream

(2) 60° with downstream

(3) 120° with downstream

(4) South

A train is moving towards east and a car is along north, both with same speed. The observed direction of car to the passenger in the train is 

(1) East-north direction

(2) West-north direction

(3) South-east direction

(4) None of these

A ball P is dropped vertically and another ball Q is thrown horizontally from the  same height and at the same time. If air resistance is neglected, then 

(1) Ball P reaches the ground first

(2) Ball Q reaches the ground first

(3) Both reach the ground at the same time

(4) The respective masses of the two balls will decide the time

A frictionless wire \(AB\) is fixed on a sphere of radius \(R\). A very small spherical ball slips on this wire. The time taken by this ball to slip from \(A\) to \(B\) is:
          
1. \(\frac{2 \sqrt{g R}}{g \cos \theta}\)
2. \(2 \sqrt{g R} . \frac{\cos \theta}{g}\)
3. \(2 \sqrt{\frac{R}{g}}\)
4. \(\frac{g R}{\sqrt{g\cos \theta}}\)