A particle moves in the x-y plane with velocity vx=8t-2 and vy=2. If it passes through the point x=14 and y=4 at t=2 sec. The equation of the path is

(A)  x=y2-y+2

(B)  x=y+2

(C)  x=y2+2

(D)  x=y2+y+2

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A motor boat of mass m moving along a lake with velocity V0. At t=0, the engine of the boat is shut down. Magnitude of resistance force offered to the boat is equal to rV. (V is instantaneous speed). What is the total distance covered till it stops completely? Hint: Fx=mVdVdx=-rV

(A)  mV0/r

(B)  3 mV0/2r

(C)  mV0/2r

(D)  2mV0/r

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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.

Initial velocity of the particle is

(A)  1 m/s

(B)  3 m/s

(C)  12 m/s

(D)  20 m/s

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Differentiation
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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.

Initial acceleration of the particle is

(A)  Zero

(B)  1 m/s2

(C)  -3 m/s2

(D)  -6 m/s2

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Differentiation
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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

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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

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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

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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°

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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

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