If the acceleration a(t) = 4t+6, the velocity of a particle starting from rest is: here, a=dvdt

1. 2t+6

2. 4

3. 0

4. 2t2+6t

Subtopic:  Integration |
 75%
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A force of F(x)=2x2+3 N is applied to an object. How much work is done, in Joules, moving the object from x=1 to x=4 meters? work=abF(x) dx

1. 113 J

2. 51 J

3. 53 J

4. 1643 J

Subtopic:  Integration |
 73%
From NCERT
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A car has a certain displacement between 0 seconds and 2 seconds. If we defined its velocity as v(t)=6t-5, then the displacement in meters is: Here, v=dsdt

1. 1 m

2. 2 m

3. 3 m

4. 4 m

Subtopic:  Integration |
 87%
From NCERT
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The relation between time t and distance x is t=ax2+bx, where a and b are constants, the acceleration is here, v=dxdt and a=d2xdt2

(1) 2b v3

(2) -2 ab v2

(3) 2 av2

(4) -2 av3

Subtopic:  Differentiation |
From NCERT
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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 |
 85%
From NCERT
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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 |
 84%
From NCERT
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The area of a blot of ink, A, is growing such that after t seconds, \(A=3t^2+\frac{t}{5}+7~m^2\). Then the rate of increase in the area at t= 5s will be :

1. 30.1 m2/s

2. 30.2 m2/s

3. 30.3 m2/s

4. 30.4 m2/s

Subtopic:  Differentiation |
 80%
From NCERT
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A particle starts rotating from rest and its angular displacement is given by θ=t240+t5. Then, the angular velocity ω=dt at the end of 10 s will be :

1. 0.7

2. 0.6

3. 0.5

4. 0

Subtopic:  Differentiation |
 81%
From NCERT
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The value of x=x=RGMmx2 dx is

1. GMmR

2. 2GMmR

3. -GMmR

4. -2GMmR

Subtopic:  Integration |
 71%
From NCERT
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0QqCdq, where C is a constant, can be expressed as:

1. Q2C

2. -Q22C

3. -Q2C

4. Q22C

Subtopic:  Integration |
 82%
From NCERT
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