If the distance 's' travelled by a body in time 't' is given by s=at+bt2 then the acceleration equals

(1)  2at3+2b

(2)  2st3

(3)  2b-2at3

(4)  st2

Subtopic:  Differentiation |
 74%
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The velocity of a particle moving on the x-axis is given by v=x2+x where v is in m/s and x is in m. Find its acceleration in m/s2 when passing through the point x=2m.

1.  0

2.  5

3.  11

4.  30

Subtopic:  Differentiation |
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A particle moves in the XY plane and at time t is at the point whose coordinates are t2, t3-2t. Then at what instant of time, will its velocity and acceleration vectors be perpendicular to each other?

(1)  1/3 sec

(2)  2/3 sec

(3)  3/2 sec

(4)  never

Subtopic:  Scalar Product |
 61%
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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

Subtopic:  Differentiation |
 76%
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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^

Subtopic:  Resultant of Vectors |
 84%
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A=4i+4j-4k and B=3i+j+4k, then angle between vectors A and B is:

(1)  180°

(2)  90°

(3)  45°

(4)  0°

Subtopic:  Resultant of Vectors |
 77%
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If a curve is governed by the equation y=sinx, then the area enclosed by the curve and x-axis between x =0 and x =π is (shaded region) :

              

1. 1 unit

2. 2 units

3. 3 units

4. 4 units

Subtopic:  Integration |
 58%
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The acceleration of a particle starting from rest varies with time according to relation, a=α t+β. The velocity of the particle at time instant t is: (\(Here, a=\frac{dv}{dt}\))

1. αt2+βt

2. αt2+βt2

3. αt22+βt

4. 2αt2+βt

Subtopic:  Integration |
 85%
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The displacement of the particle is zero at t=0 and at t=t it is x. It starts moving in the x-direction with a velocity that varies as v=kx, where k is constant. The velocity will : (Here, \(v=\frac{dx}{dt}\))

1. vary with time.

2. be independent of time.

3. be inversely proportional to time.

4. be inversely proportional to acceleration.

Subtopic:  Integration |
 51%
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The acceleration of a particle is given as a=3x2.  At t = 0, v = 0 and x = 0. It can then be concluded that the velocity at t = 2 sec will be: (Here, \(a=v\frac{dv}{dx}\))

1.  0.05 m/s

2. 0.5 m/s

3. 5 m/s

4. 50 m/s 

Subtopic:  Integration |
 62%
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