The displacement of particle is zero at t=0 and at t=t it is x. It starts moving in the x direction with velocity, which varies as $v=k\sqrt{x}$, where k is constant. The velocity-

1. varies with time

2. is independent to time

3. inversely proportional to time

4. inversely proportional to acceleration

Concept Questions :-

Integration

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The acceleration of a particle is given as $a=3{x}^{2}$. At t=0, v=0, x=0, the velocity at t =2 sec will be-

1. 0.05 m/s

2. 0.5 m/s

3. 5 m/s

4. 50 m/s

Concept Questions :-

Integration

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The acceleration of a particle is given by a=3t and at t=0, v=0, x=0. The velocity and displacement at t = 2 sec will be-

1. 6 m/s, 4 m

2. 4 m/s, 6 m

3. 3 m/s, 2 m

4. 2 m/s, 3 m

Concept Questions :-

Integration

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The 9 kg block is moving to the right with a velocity of 0.6 m/s on a horizontal surface when a force F, whose time variation is shown in the graph, is applied to it at time t = 0. Calculate the velocity v of the block when t= 0.4s. The coefficient of kinetic fricton is ${\mu}_{k}=0.3$. **[ This question is only for Dropper and XII batch]**

1. 0.6 m/s

2. 1.2 m/s

3. 1.8 m/s

4. 2.4 m/s

Concept Questions :-

Integration

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A 10 kg mass moves along x-axis. Its acceleration as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from x=0 to x=8 cm** [This question is only for Dropper and XII batch]**

1. $6\times {10}^{-2}J$

2. $7\times {10}^{-2}J$

3. $8\times {10}^{-2}J$

4. $9\times {10}^{-2}J$

Concept Questions :-

Integration

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The relationship between force and position is shown in the figure given (in one dimensional case). Find the work done by the force in displaying a body from x= 1 cm to x= 5cm is ** [This question is only for Dropper and XII batch]**

1. 10 erg

2. 20 erg

3. 30 erg

4. 40 erg

Concept Questions :-

Integration

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The graph between the resistive force F acting on a body and the distance covered by the body is shown in the figure. The mass of the body is 25 kg and initial velocity is 2 m/s. When the distance covered by the body is 4 m, its kinetic energy would be ** [This question is only for Dropper and XII batch]**

1. 50 J

2. 40 J

3. 20 J

4. 10 J

Concept Questions :-

Integration

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A long spring is stretched by 2 cm, its potential energy is U. If the spring is streched by 10 cm, find the potential energy stored in it. ** [This question is only for Dropper and XII batch]**

1. 10 U

2. 15 U

3. 20 U

4. 25 U

Concept Questions :-

Integration

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A spring of spring constant $5\times {10}^{3}N/m$ is stretched initially by 5 cm from the unstretched position. Find the work required to stretch it further by another 5 cm is ** [This question is only for Dropper and XII batch]**

1. 15 J

2. 18.75 N .m

3. 20 J

4. 22.75 N .m

Concept Questions :-

Integration

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A constant force F is applied on a body. The power (P) generated is related to the time elapsed (t) as

**[This question is only for Dropper and XII batch]**

1. $P\propto {t}^{2}$

2. $P\propto t$

3. $P\propto \sqrt{t}$

4. $P\propto {t}^{3/2}$

Concept Questions :-

Integration

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