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 |
 72%
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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%
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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 |
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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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The current through a wire depends on time as \(i = (2+3t)~\text{A}\). The charge that crosses through the wire in \(10\) seconds is: \(\left(\text{Instantaneous current,}~i= \frac{dq}{dt} \right)\)
1. \(150~\text{C}\)
2. \(160~\text{C}\)
3. \(170~\text{C}\)

4. None of there

Subtopic:  Integration |
 84%
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The area of a blot of ink, \(A\), is growing such that after \(t\) seconds, \(A=\left(3t^2+\frac{t}{5}+7\right)\text{m}^2\). Then the rate of increase in the area at \(t = 5~\text{s}\) will be:
1. \(30.1~\text{m}^2/\text{s}\)
2. \(30.2~\text{m}^2/\text{s}\)
3. \(30.3~\text{m}^2/\text{s}\)
4. \(30.4~\text{m}^2/\text{s}\)

Subtopic:  Differentiation |
 80%
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A particle starts rotating from rest and its angular displacement is given by \(\theta = \frac{t^2}{40}+\frac{t}{5}\). Then, the angular velocity \(\omega = \frac{d\theta}{dt}\) at the end of \(10~\text{s}\) will be:
1. \(0.7\)
2. \(0.6\)
3. \(0.5\)
4. \(0\)

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

1. GMmR

2. 2GMmR

3. -GMmR

4. -2GMmR

Subtopic:  Integration |
 72%
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0QqCdq, where C is a constant, can be expressed as:

1. Q2C

2. -Q22C

3. -Q2C

4. Q22C

Subtopic:  Integration |
 83%
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If the force on an object as a function of displacement is \(F \left(x\right) = 3 x^{2} + x\), what is work as a function of displacement \(w(x)\)\(\left(w= \int f\cdot dx\right)\) Assume \(w(0)= 0\) and force is in the direction of the object's motion.
1. \(\frac{3 x^{3}}{2} + x^{2}\)
2. \(x^{3} + \frac{x^{2}}{2}\)
3. \(6x+1\)
4. \(3 x^{2} + x\)

Subtopic:  Integration |
 86%
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