The x and y coordinates of a particle at any time t are given by $x=7t+4{t}^{2}$ and y = 5t, where x and y are in metre and t in seconds. The acceleration of particle at t = 5s is

(1) Zero

(2) 8 m/s2

(3) 20 m/s2

(4) 40 m/s2

Concept Questions :-

Acceleration
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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

Concept Questions :-

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 is

(1) 5 min

(2) 60 min

(3) 20 min

(4) 30 min

Concept Questions :-

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

Concept Questions :-

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

Concept Questions :-

Relative 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

Concept Questions :-

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

Concept Questions :-

Circular motion
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If a particle moves in a circle describing equal angles in equal times, its velocity vector

(1) Remains constant

(2) Changes in magnitude

(3) Changes in direction

(4) Changes both in magnitude and direction

Concept Questions :-

Circular motion
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A motor cyclist going round in a circular track at constant speed has

(1) Constant linear velocity

(2) Constant acceleration

(3) Constant angular velocity

(4) Constant force

Concept Questions :-

Circular motion
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A particle P is moving in a circle of radius ‘a’ with a uniform speed v. C is the centre of the circle and AB is a diameter. When passing through B the angular velocity of P about A and C are in the ratio

(1) 1 : 1

(2) 1 : 2

(3) 2 : 1

(4) 4 : 1

Concept Questions :-

Circular motion