A weight hanging from a spring is stretched down 3 cm beyond its rest position and released at time t=0 to bob up and down. Its position at any later time t is s=3cos(t). Then its velocity at time t is velocity =dsdt

(1) cost

(2) 3cost

(3) 3sint

(4) -3sint

Subtopic:  Differentiation |
 81%
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The position of a particle is given by s(t)=2t2+1t+1. Then, at t = 2, its velocity is :vinst=dsdt

1. 163

2. 159

3. 153

4. None of these

Subtopic:  Differentiation |
 56%
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The instantaneous velocity at t=π2 of a particle whose positional equation is given by x(t)=12 cos2(t) is vinst=dxdt -

(1) 0

(2) -24

(3) 24

(4) -122

Subtopic:  Differentiation |
 54%
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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 |
 77%
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If x=3tan(t) and y=sec(t), then the value of d2ydx2 at t=π4 is:

1. 3

2. 1182

3. 1

4. 1/6

Subtopic:  Differentiation |
 58%
From NCERT
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A particle's position as a function of time is given by x=-t2+6t+3. The maximum value of the position co-ordinate of the particle is:

1. 8

2. 12

3. 3

4. 6

Subtopic:  Differentiation |
 64%
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A gas undergoes a process where pressure P=3V4, at every instant, here V is the volume. Find an expression for the bulk modulus (B) in terms of volume if it is related to P and V as B=-VdPdV.

(1) -3V3

(2) -12 V3

(3) -12 V4

(4) -12 V5

Subtopic:  Differentiation |
 65%
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The current in a circuit is defined as I=dqdt. The charge (q) flowing through a circuit, as a function of time (t), is given by q=5t2-20t+3. The minimum charge flows through the circuit at:

1. t=4 sec

2. t=2 sec

3. t= 6 sec

4. t=3 sec

Subtopic:  Differentiation |
 87%
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The current in a circuit is defined as I=dqdt. If the charge (q) flowing through a circuit is given by q=(t2-3t+4), current flowing through the circuit is equal to zero at:

1. t=3 sec

2. t=2 sec

3. t=1.5 sec

4. t=15 sec

Subtopic:  Differentiation |
 86%
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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 |
 77%
From NCERT
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