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
The position of a particle is given by \(s\left( t\right) = \frac{2 t^{2} + 1}{t + 1}\). Then, at \(t= 2\), its velocity is: \(\left(v_{inst}= \frac{ds}{dt}\right)\)
1. \(\frac{16}{3}\)
2. \(\frac{15}{9}\)
3. \(\frac{15}{3}\)
4. None of these
If acceleration of a particle is given as a(t) = sin(t)+2t.
Then the velocity of the particle will be:
(acceleration )
1. \(-\cos(t)+ \frac{t^2}{2}\)
2. \(-\sin(t)+ t^2\)
3. \(-\cos(t)+ t^2\)
4. None of these
If \(x= 3\tan(t)\) and \(y = \sec (t)\), then the value of \(\frac{d^{2} y}{d x^{2}}~\text{at}~t = \frac{\pi}{4}\) is:
1. \(3\)
2. \(\frac{1}{18\sqrt{2}}\)
3. \(1\)
4. \(\frac{1}{6}\)
A particle's position as a function of time is given by .
The maximum value of the position co-ordinate of the particle is:
1. \(8\)
2. \(12\)
3. \(3\)
4. \(6\)
The equation of position (\(x\)) of a particle is given by The maximum velocity of the particle is, if velocity is defined as :
1. +56 m/s
2. +46 m/s
3. +36 m/s
4. +26 m/s
The current in a circuit is defined as . The charge (q) flowing through a circuit, as a function of time (t), is given by . The minimum charge flows through the circuit at:
1. \(t = 4~\text{s}\)
2. \(t = 2~\text{s}\)
3. \(t = 6~\text{s}\)
4. \(t = 3~\text{s}\)
Work done by a force (\(F\)) in displacing a body by dx is given by W=. If the force is given as a function of displacement (\(x\)) by \(F \left(x\right) = \left( x^{2} - 2 x + 1\right) \text{N}\), 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
The impulse due to a force on a body is given by \(I=\int Fdt\). If the force applied on a body is given as a function of time \((t)\) as \(F = \left(3 t^{2} + 2 t + 5\right) \text{N}\), then impulse on the body between \(t = 3~\text{s}\) to \(t =5~\text{s}\) is:
1. \(175\) kg-m/sec
2. \(41\) kg-m/sec
3. \(216\) kg-m/sec
4. \(124\) kg-m/sec
If is the angle between vectors , then which of the following is the unit vector perpendicular to ?
1.
2.
3.
4.