Uniform and Non Uniform

Q.

A train is travelling at a speed of$90km{h}^{-1}$. Brakes are applied so as to produce a uniform acceleration of$-0.5m{s}^{-2}$. Find how far the train will go before it is brought to rest.

Q.

A body of mass $2kg$ is driven by an engine delivering a constant power of $1J{s}^{-1}$. The body starts from rest and moves in a straight line. After $9s$ the body has moved a distance (in $m$) _____________.

Q.

The velocity v of a particle depends upon the time t according to the equation $v=a+bt+\frac{c}{d+t}$.The dimensions of a, b, c and d are

1. \[LT^{-1} ], [LT^{-2} ], [L], [T]\)
2. $\left[L{T}^{-2}\right],\left[L\right],\left[T\right],\left[L{T}^{-1}\right]$
3. $\left[T\right],\left[L\right],\left[L{T}^{-1}\right],\left[L{T}^{-2}\right]$
4. $\left[L\right],\left[T\right],\left[L{T}^{-1}\right],\left[L{T}^{-2}\right]$

Q.

What is Retardation?

Q.

A body, whose momentum is constant, must have constant

1. Force

2. Velocity

3. Acceleration

4. All of these

Q.

A motorcyclist moving with uniform retardation takes 10s and 20s to travel successive quarter kilometer.How much farther will he travel before coming to rest?

Q. The speed of a particle moving in a circle of radius r = 2 m varies with time t as $v=t^2$ where t is in second and v in m/s. The net acceleration at t =2 s is

1. 
2. 
3. 
4. 

Q. A point moves in a straight line so that its displacement $x$ at time $t$ is given by equation $x^2=t^2+1$. Its acceleration is:

1. $\frac{1}{x^3}$
2. $-\frac{1}{x^3}$
3. $\frac{1}{x}$
4. $-\frac{1}{x^2}$

Q. A person driving a car at a speed 72 km per hour, sees a boy crossing the road. If the distance moved by the car before the person applies brakes is 5 m, find the reaction time of the person.

Q. In the one-dimensional motion of a particle, the relation between position $x$ and time $t$ is given by $x^2+2x=t$ , where $x>0$. Choose the correct statement.

1. The retardation of the particle is $\frac{1}{4(x+1{)}^3}$.
2. The velocity of the particle is $\frac{1}{(x+1{)}^3}$.
3. Both are wrong
4. Both are correct

Q.

The negative acceleration is called _______ .

Q. Two trains , each having a speed of 30km/h , r headed at each other on the same track. A bird that can fly 60km/h flies off the front of 1 train when they were 60km apart and heads directly to the other train . On reaching the
train , the bird flies back to the first train.
What is the total distance the bird travels
before the train collide??

Q. The displacement travelled by a particle in a straight-line motion is directly proportional to $t^{1/2}$, where $t=$ time elapsed. What is the nature of motion?

1. Increasing acceleration
2. Decreasing acceleration
3. Increasing retardation
4. Decreasing retardation

Q. The average velocity of a body moving with uniform acceleration travelling a distance $3.06\text{m}$ is $0.34\text{m/s}$. If the change in velocity of the body is $0.18\text{m/s}$ during this time, its uniform acceleration is

1. $0.01{\text{m/s}}^2$
2. $0.02{\text{m/s}}^2$
3. $0.04{\text{m/s}}^2$
4. $0.03{\text{m/s}}^2$

Q. A particle moves along x-axis and its acceleration at any time $t$ is $a=2sin\left(\pi t\right)$, where $t$ is in seconds and $a$ is in $m/s^2$. The initial velocity of particle (at time $t=0$) is $u=0$.
Then the distance travelled (in meters) by the particle from time $t=0$ to $t=t$ will be

1. $\frac{2}{{\pi }^2}\sin \pi t-\frac{2t}{\pi }$
2. $\frac{2t}{\pi }$
3. None of these
4. $-\frac{2}{{\pi }^2}\sin \pi t+\frac{2t}{\pi }$

Q.

Explain the following types of motion with one example of each

Acceleration is zero.-

Q.

Find the time period of the motion of the particle shown in figure (12-E14). Neglect the small effect of the bend near the bottom.

Q. A particle moves along x-axis and its acceleration at any time $t$ is $a=2sin\left(\pi t\right)$, where $t$ is in seconds and $a$ is in $m/s^2$. The initial velocity of particle (at time $t=0$) is $u=0$. The distance travelled (in meters) by the particle from time $t=0$ to $t=1\text{s}$ will be

1. $\frac{2}{\pi }$
2. $\frac{4}{\pi }$
3. $\frac{1}{\pi }$
4. None of these

Q. Express $L$ (length) in terms of $G,h$ and $c$ -
Here $G$ is universal gravitational constsnt, $h$ is plank's constant, $c$ is speed of light

1. $G^{-\frac{1}{2}}{h}^{\frac{1}{2}}{c}^{\frac{1}{2}}$
2. $G^{\frac{1}{2}}{h}^{\frac{1}{2}}{c}^{-\frac{3}{2}}$
3. $G^{\frac{1}{2}}{h}^{\frac{1}{2}}{c}^{-\frac{5}{2}}$
4. $Ghc$

Q. Block of mass 10kg is moving on inclined plane of angle 37 degree with constant velocity 10m/s the coeficcient of kinetic friction between inclined plane and block is

Q. A particle is resting on a smooth horizontal floor. At $t=0$, a horizontal force starts acting on it. Magnitude of the force increases with time according to law $F=\alpha t$, where $\alpha$ is a constant. For the figure shown, which of the following statements is/are correct ?

1. Curve 1 may represent acceleration against time graph
2. Curve 2 may represent velocity against time graph
3. Curve 2 may represent velocity against acceleration graph
4. None of these

Q. Each of the four particles move along $x$ axis. Their coordinate (in meters) as function of time (in seconds) are given by
Particle 1: $x\left(t\right)=3.5-2.7t^3$
Particle 2: $x\left(t\right)=3.5+2.7t^3$
Particle 3: $x\left(t\right)=3.5+2.7t^2$
Particle 4: $x\left(t\right)=3.5-3.4t-2.7t^2$
Which of these particles are speeding up for $t>0$?

1. All four
2. Only 1
3. Only 2 and 3
4. Only 2, 3 and 4

Q. The velocity of a particle moving in the positive direction of $x-$ axis varies as $v=10\sqrt{x}$ ($v$ is in ${\text{ms}}^{-1},x$ is in $m$). Assuming that at $t=0,$ particle was at $x=0$. Then,

1. The initial velocity of the particle is zero
2. The initial velocity of the particle is $2.5{\text{ms}}^{-1}$
3. The acceleration of the particle is $2.5{\text{ms}}^{-2}$
4. The acceleration of the particle is $50{\text{ms}}^{-2}$

Q. A particle starts its $2D$ motion from origin such that its velocity in $x-$direction remains constant at $3\text{m/s}$ and in $y-$direction its acceleration varies with time as $a_y=(t^2+2){\text{m/s}}^2$. Find the position vector of particle at $t=2\text{sec}$

1. $\overrightarrow{r}=(6\hat{i}+5.33\hat{j})\text{m}$
2. $\overrightarrow{r}=(6\hat{i}+1.33\hat{j})\text{m}$
3. $\overrightarrow{r}=(6\hat{i}-5.33\hat{j})\text{m}$
4. $\overrightarrow{r}=(6\hat{i}-1.33\hat{j})\text{m}$

Q. A rod of mass M is placed over smooth horizontal surface. Forces 2F, F are applied at the ends of the rod as shown. If length, cross-sectional area and Youngs modulus of rod are L, A and Y respectively, then total elongation of rod will be (F=Mg)


e 

Q. In a hydrogen atom, an electron of mass $m$ and charge $e$ revolves in an orbit of radius $r$ making $n$ revolutions per second. If the mass of hydrogen nucleus is $M$, the magnetic moment associated with the orbital motion of electron is

1. $\frac{\pi ne{r}^{2}m}{M+m}$
2. $\pi ne{r}^2$
3. $\frac{\pi ne{r}^2}{m}$
4. $\frac{\pi ne{r}^{2}m}{M}$

Q.

A thief with a stolen car passes through a police check post at his top speed of 90 km per hour a motorcycle cop reacting after 2 seconds accelerates from rest at 5 metre per second square is top speed being 108 km per hour find the maximum separation between police man and thief

Q.

Let v and a denote the velocity and acceleration respectively of a body in one dimensional motion.Then which of the statements are correct?

A) speed must decrease when a<0

B)speed must increase when a>0

C)speed will increase when both v and a are less than zero

D)speed will decrease when v<0 and a>0

It is a multi correct question

Q. If the dimensions of a physical quantity are given by $M^a{L}^b{T}^c$, then the physical quantity will be:

1. Velocity if a = 1, b = 0, c = -1
2. Force if a = 0, b = –1, c = -2
3. Pressure if a = 1, b = –1, c = -2
4. Acceleration if a = 1, b = 1, c = -2

Q. For a particle moving along a straight line, the position $x$ depends on time $t$ as $x=A{t}^3+B{t}^2+Ct+D$. The ratio of its initial velocity to its initial acceleration will be

1. $\frac{C}{B}$
2. $\frac{D}{C}$
3. $\frac{C}{2B}$
4. $\frac{2B}{3A}$