A body is moving according to the equation x=at+bt2-ct3 where x = displacement and a, b and c are constants. The acceleration of the body is

(A)  a+2bt

(B)  2b+6ct

(C)  2b-6ct

(D)  3b-6ct2

Concept Questions :-

Differentiation
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A particle moves along X-axis in such a way that its X coordinate  varies with time t according to the equation x=2-5t+6t2m. The initial velocity of the particle is

(A)  -5 m/s

(B)  6 m/s

(C)  3 m/s

(D)  3 m/s

Concept Questions :-

Differentiation
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If the momentum of a particle is given by P=(180-8t) kg m/s, then its force will be

(A)  Zero

(B)  8 N

(C)  -8 N

(D)  4 N

Concept Questions :-

Differentiation
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A particle moves along x-axis as x=4t-2+at-22

Which of the following is true?

1.  The initial velocity of the particle is 4.

2.  The acceleration of the particle is 2a.

3.  The particle is at the origin at t=0.

4.  None of these

Concept Questions :-

Differentiation
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The maximum value of 7+6x-9x2 is

(A)  8

(B)  -8

(C)  4

(D)  -4

Concept Questions :-

Differentiation
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If fx=x2-2x+4, then f(x) has

1.  a minimum at x=1

2.  a maximum at x=1

3.  no extreme point

4.  no minimum

Concept Questions :-

Differentiation
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A particle is moving along x-axis. The velocity v of particle varies with its position x as v=1x. Find velocity of particle as a function of time t given that at t=0, x=1 .

1.  v=2t+1

2.  v=12t+1

3.  v=1t

4.  None of these

Concept Questions :-

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A vector A is directed along 30° west of north direction and another vector B along 15° south of east. Their resultant cannot be in ____________ direction.

(A)  North

(B)  East

(C)  North-East

(D)  South

Concept Questions :-

Resultant of Vectors
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ABCD is a quadrilateral. Forces BA, BC, CD & DA act at a point. Their resultant is 

(A)  2 AB

(B)  2 DA

(C)  zero vector

(D)  2 BA

Concept Questions :-

Resultant of Vectors
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The resultant of the forces P and Q is R. If Q is double then the resultant also doubles in magnitude. Find the angle between P and Q.

(A)  cos θ=Q2P

(B)  cos θ=-4Q3P

(C)  cos θ=-2Q3P

(D)  cos θ=-3P4Q

Concept Questions :-

Resultant of Vectors
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