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) $\sqrt{\frac{a}{2b}}$

Subtopic:  Acceleration |
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A body projected with velocity u with an angle of projection $\theta$. Change in velocity after the time (t) from the projection is:

(1) gt

(2) $\frac{1}{2}g{t}^{2}$

(3) u sin$\theta$

(4) u cos$\theta$

Subtopic:  Projectile Motion |
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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

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

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

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

(3) $8\stackrel{^}{j}$

(4) $6\stackrel{^}{i}$

Subtopic:  Relative Motion |
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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

Subtopic:  Relative Motion |
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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

Subtopic:  Relative Motion |
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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

Subtopic:  Relative Motion |
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An aeroplane is moving with a velocity u. It drops a packet from a height h. The time t taken by the packet in reaching the ground will be

(1) $\sqrt{\left(\frac{2g}{h}\right)}$

(2) $\sqrt{\left(\frac{2u}{g}\right)}$

(3) $\sqrt{\left(\frac{h}{2g}\right)}$

(4) $\sqrt{\left(\frac{2h}{g}\right)}$

Subtopic:  Projectile Motion |
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If the body is moving in a circle of radius r with a constant speed v, its angular velocity is

(1) v2/r

(2) vr

(3) v/r

(4) r/v

Subtopic:  Circular Motion |
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Two racing cars of masses m1 and m2 are moving in circles of radii r1 and r2 respectively. Their speeds are such that each makes a complete circle in the same duration of time t. The ratio of the angular speed of the first to the second car is

(1) m1 : m2

(2) r1 : r2

(3) 1 : 1

(4) m1 r1 : m2 r2

Subtopic:  Circular Motion |
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