Differentiation

Q.

At a certain temperature, the r.m.s velocity for $O_2$ is 400 m/sec. At the same temperature, the r.m.s velocity for $H_2$ molecules will be

1. 25 m/sec

2. 1600 m/sec

3. 6400 m/sec

4. 100 m/sec

Q.

The velocity of a particle at time $t$ is given by the relation $v=6t-\left(\frac{t^2}{6}\right)$. The distance travelled in $3sec$ is, if $s=0$at $t=0$

1. $\raisebox{1ex}{$39$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

2. $\raisebox{1ex}{$57$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

3. $\raisebox{1ex}{$51$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

4. $\raisebox{1ex}{$33$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

Q. A man walking with a speed of 3 m/s passes under a lamp hanging at a height of 8 m above the ground. If the height of the man is 2 m, the velocity in m/s with which the edge of the shadow of the mans head moves over the ground is

Q. Find the local maxima and minima of the function $y=x^3-3x+2$.

1. $6$ , $3$
2. $4$ , $0$
3. $8$ , $4$
4. $0$ , $4$

Q. A lamp post is fixed at point (0, 0, 5m). A man is moving with cons†an t velocity 6 m/s along a line \sqrt3x. Height of man is 2m and initially the man is at origin. What is The velocity of edge of his shadow along the line of motion of man vectorically

Q. A function is given as $y=5x^2-10x$, then

1. Maximum value of y is 10
2. Minimum value of y is -5
3. Maximum value of y is 0
4. Maximum value of y occurs at x = 1

Q. The area $A$ of a circle is related to its radius by the equation
$A=\pi r^2$. The change in area with respect to the radius is $x\times \pi$ $m$. When the radius is $5m$, find the value of $x$.

Q. A particle, initially at rest is subject to two forces; one is constant, the other is a retarding force proportional to the particle velocity. In the subsequent motion of the particle,

1. the acceleration will increase from zero to a constant value
2. the acceleration will remain constant with respect to time
3. the velocity will increase from zero to a maximum and then decrease
4. the velocity will increase from zero to a constant value

Q. A man walking with a speed of 3 m/s passes under a lamp hanging at a height of 8 m above the ground. If the height of the man is 2 m, the velocity in m/s with which the edge of the shadow of the man's head moves over the ground is

Q. The position of the particle is given by $x\left(t\right)=(4t^2-3t+2t^3)$, its acceleration will be

1. $4t+2t^2$
2. $12t^2+8t$
3. $8t-3+6t^2$
4. $12t+8$

Q. The position vector of a moving particle in $x-y$ plane can be represented as $\overrightarrow{r}=\left(2t\hat{i}+2t^2\hat{j}\right)m$, where $t$ represents the time instant. The rate of change of $\theta$ at time $t=2s$. (where $\theta$ is the angle which its velocity vector makes with positive $x-$axis)

1. $\frac{2}{5}rad/s$
2. $\frac{2}{17}rad/s$
3. $2rad/s$
4. $4rad/s$

Q. Power supplied to a particle of mass $2\text{kg}$ varies with time as $P=\frac{3t^2}{2}$ watt. Here $t$ is in second. If velocity of particle at $t=0$ is $v=0$. The velocity of particle at time $t=2$ s will be

1. $1\text{m/s}$
2. $4\text{m/s}$
3. $2\text{m/s}$
4. $2\sqrt{2}\text{m/s}$

Q. The motion of a particle along a straight line is described by the equation $x=6+27t-t^3$.
Find the time when $K.E$ of the particle is zero.

1. $3s$
2. $2s$
3. $4s$
4. $1s$

Q. The maximum speed with which a vehicle can take the safely circular turn on a horizontal flat rough road is (where symbols have their usual meanings).

1. $\mu \sqrt{rg}$
2. $\sqrt{\frac{rg}{\mu }}$
3. $\sqrt{rg}$
4. $\sqrt{rg\mu }$