A particle is moving along positive x-axis. Its position varies as x=t3-3t2+12t+20, where x is in meters and t is in seconds.

Velocity of the particle when its acceleration zero is

(A)  1 m/s

(B)  3 m/s

(C)  6 m/s

(D)  9 m/s

Concept Questions :-

Differentiation
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Two forces F1=2i^+2j^ N and F2=3j^+4k^ N are acting on a particle.

The resultant force acting on particle is:

(A)  2i^+5j^+4k^

(B)  2i^-5j^-4k^

(C)  i^-3j^-2k^

(D)  i^-j^-k^

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Two forces F1=2i^+2j^ N and F2=3j^+4k^ N are acting on a particle.

The angle between F1 & F2 is:

(A)  θ=cos-1325

(B)  θ=cos-1352

(C)  θ=cos-1235

(D)  θ=cos-135

Concept Questions :-

Resultant of Vectors
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Two forces F1=2i^+2j^ N and F2=3j^+4k^ N are acting on a particle.

The magnitude of the component of force F1 along force F2 is:

(A)  56

(B)  53

(C)  65

(D)  52

Concept Questions :-

Resultant of Vectors
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A=4i+4j-4k and B=3i+j+4k, then angle between vectors A and B is:

(A)  180°

(B)  90°

(C)  45°

(D)  0°

Concept Questions :-

Resultant of Vectors
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A curve is governed by the equation y=sinx, then what is the area enclosed by the curve and x-axis between x =0 and x =π is (shaded region)

       

1. 1 units

2. 2 units

3. 3 units

4. 4 units

Concept Questions :-

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Calculate the area of disk of radius 'a' using integration

1. πa22

2. πa2

3. 32πa2

4. 2πa2

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The acceleration of a particle starting from rest varies with time according to relation, a=α t+β. Find the velocity of the particle at time instant t.

1. αt2+βt

2. αt2+βt2

3. αt22+βt

4. 2αt2+βt

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The displacement of particle is zero at t=0 and at t=t it is x. It starts moving in the x direction with velocity, which varies as v=kx, where k is constant. The velocity-

1. varies with time

2. is independent to time

3. inversely proportional to time

4. inversely proportional to acceleration

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The acceleration of a particle is given as a=3x2. At t=0, v=0, x=0, the velocity at t =2 sec will be-

1.  0.05 m/s

2. 0.5 m/s

3. 5 m/s

4. 50 m/s 

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