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 |
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The acceleration of a particle is given by a=3t  at t=0, v=0, x=0. The velocity and displacement at t = 2 sec will be: (\(Here, a=\frac{dv}{dt}~ and~v=\frac{dx}{dt}\))

1. 6 m/s, 4 m

2. 4 m/s, 6 m

3. 3 m/s, 2 m

4. 2 m/s, 3 m

Subtopic:  Integration |
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Given velocity v(t)=52t+3. Assume s(t) is measured in meters and t is measured in seconds. If s(0)=0, the position s(4) at t=4s is:  Given, v=dsdt

1. 30

2. 31

3. 32

4. 33

Subtopic:  Integration |
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If the force on an object as a function of displacement is F(x)=3x2+x, what is work as a function of displacement w(x) W=(fdx). Assume W(0)=0 and force is in the direction of the object's motion.

1. 3x32+x2

2. x3+x22

3. 6x+1

4. 3x2+x

Subtopic:  Integration |
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The current through a wire depends on time as i =(2+3t) A. The charge that crosses through the wire in 10 seconds is: Instantaneous current, i=dqdt
1. 150 C
2. 160 C
3. 170 C
4. None of there

Subtopic:  Integration |
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0QqCdq, where C is a constant, can be expressed as:

1. Q2C

2. -Q22C

3. -Q2C

4. Q22C

Subtopic:  Integration |
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The impulse due to a force on a body is given by I=Fdt. If the force applied on a body is given as a function of time (t) as F=(3t2+2t+5)N, then impulse on the body between t=3 sec to t = 5 sec is:

1. 175 kg-m/sec

2. 41 kg-m/sec

3. 216 kg-m/sec

4. 124 kg-m/sec

Subtopic:  Integration |
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The work done by gravity exerting an acceleration of -10 m/s2 for a 10 kg block down 5 m from its original position with no initial velocity is:

(Fgrav=mass ×acceleration and W=abF(x)dx)

1. 250 J

2. 500 J

3. 100 J

4. 1000 J

Subtopic:  Integration |
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Work done by a force (F) in displacing a body by dx is given by W=Fx.dx. If the force is given as a function of displacement (x) by F(x)=(x2-2x+1)N, then work done by the force from x=0 to x=3 m is:

1. 3 J

2. 6 J

3. 9 J

4. 21 J

Subtopic:  Integration |
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If acceleration of a particle is given as a(t)=sin(t)+2t. Then the velocity of the particle will be:

(acceleration a=dvdt)

1. -cos(t)+t22

2. -sin(t)+t2

3. -cos(t)+t2

4. None of these

Subtopic:  Integration |
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