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
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. \(30.4~\text{m}^2/\text{s}\)
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. \(0\)
, where C is a constant, can be expressed as:
1.
2.
3.
4.
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. \(3 x^{2} + x\)
The velocity of a rocket, in metres per second, \(t\) seconds after it was launched is modelled by \(v(t)=2\sqrt{t}\). What is the total distance travelled by the rocket during the first four seconds of its launch?
1. \(\frac{16}{3}~\text{m}\)
2. \(32~\text{m}\)
3. \(\frac{32}{3}~\text{m}\)
4. \(16~\text{m}\)
The work done by gravity exerting an acceleration of \(-10\) m/ for a \(10\) kg block down \(5\) m from its original position with no initial velocity is: \(\left(F_{\text{gravitational}}= \text{mass}\times \text{acceleration and} ~w = \int^{b}_{a}F(x)dx \right)\)
1. \(250\) J
2. \(500\) J
3. \(100\) J
4. \(1000\) J
Water flows into a container of 1000 L at a rate of (180+3t) gal/min for an hour, where t is measured in minutes. Find the amount of water that flows into the pool during the first 20 minutes.
1. 4000 gal
2. 2800 gal
3. 4200 gal
4. 3800 gal
If v(t) = 3t-1 and x(2) = 1, then the original position function is:
Hint: \(\left(v \left( t \right) = \frac{d s}{d t}\right)\)
2.
3.
4. None of the above