Velocity

Q. A body covers the first $1/3$ of the distance with a velocity of $2\text{m/s}$, the next $1/3$ with $3\text{m/s}$ and the rest of the distance with $6\text{m/s}$. The average velocity in $\text{m/s}$ for covering the whole distance is (assume that the body travels with constant velocity in all the parts in a straight line)

1. $3$
2. $\frac{11}{3}$
3. $\frac{8}{3}$
4. $\frac{4}{3}$

Q. A train of length $100\text{m}$ is crossing a bridge $200\text{m}$ long in length at the speed of $72\text{kmph}$. What is the time taken by the train to cross the bridge?

1. 15 seconds
2. 10 seconds
3. 5 seconds
4. 20 seconds

Q. The position of the particle is given by $x=(3t^2-e^t)$ in $\text{m}$. The velocity $\left(\text{in m/s}\right)$ of the particle as a function of time $t$ is

1. $2t-e^t$
2. $3t+e^t$
3. $6t-e^t$
4. $6t^2-e^t$

Q. The position of the particle is given by $x=2t^2+6t+2$ in $\text{m}$. The instantaneous speed of the particle at $6\text{sec}$ is

1. $20\text{m/s}$
2. $24\text{m/s}$
3. $30\text{m/s}$
4. $36\text{m/s}$

Q. The position of the particle is given by $x=(e^t-\cos t)$ in $\text{m}$. The velocity $\left(\text{in m/s}\right)$ of the particle as a function of time $t$ is

1. $e^t-\sin t$
2. $e^t-\sec t$
3. $e^t+\tan t$
4. $e^t+\sin t$

Q. A ball of mass $m$ is suspended by a thread of length $l$. With what minimum velocity has the point of suspension to be shifted in the horizontal direction for the ball to move along the circle about the point?

1. $\sqrt{3gl}$
2. $\sqrt{5gl}$
3. $\sqrt{7gl}$
4. $\sqrt{2gl}$

Q. A body is projected up with a velocity equal to $\frac{3}{4}\text{th}$ of the escape velocity from the surface of the earth. The height it reaches is (Radius of the earth is R) :

1. $\frac{10R}{9}$
2. $\frac{9R}{7}$
3. $\frac{9R}{8}$
4. $\frac{8R}{5}$

Q. The position of a particle moving along x-axis is given by $x=(t^2-15t+10)\text{m}$, where $t$ is in second. Find the time when particle comes at rest?

1. $8.5\text{s}$
2. $7.5\text{s}$
3. $6.5\text{s}$
4. $10.5\text{s}$

Q. A string with one end fixed on a rigid wall passing over a fixed frictionless pulley at a distance of $2\text{m}$ from the wall, has a point mass $M=2\text{kg}$ attached to it at a distance of $1\text{m}$ from the wall. A mass $m=0.5\text{kg}$ attached at the free end is held at rest so that the string is horizontal between the wall and the pulley, and vertical beyond the pulley. What will be the speed which the mass $M$ will hit the wall when the mass $m$ is released? (Take $g=10{\text{m/s}}^2$)

1. $3.4\text{m/s}$
2. $4.1\text{m/s}$
3. $5.5\text{m/s}$
4. $6.6\text{m/s}$

Q. A clock has a continuously moving second's hand of $0.1\text{m}$ length. The average accelaration of the tip of the hand (in units of ${\text{ms}}^{-2}$) is of the order of :

1. ${10}^{-3}$
2. ${10}^{-4}$
3. ${10}^{-2}$
4. ${10}^{-1}$

Q. The position of a particle moving along x-axis is given by $x=(t^2-15t+10)\text{m}$, where $t$ is in second. Find the time when particle comes at rest?

1. $8.5\text{s}$
2. $7.5\text{s}$
3. $6.5\text{s}$
4. $10.5\text{s}$

Q. The phase difference between displacement and acceleration of a particle performing S.H.M is

1. $\frac{\pi }{2}$ rad
2. $2\pi$ rad
3. $\frac{3\pi }{2}$
4. $\pi$ rad

Q.

Dave walked to his friends house at a rate of $4\text{mph}$ and returned back biking at a rate of $10\text{mph}$. If it took him $18\text{minutes}$ longer to walk than to bike, what was the total distance of the round trip?

Q. The velocity of the tip of the second hand of a watch is $10\text{cm/s}$. The change in velocity of its tip in $15\text{s}$ is

1. zero
2. $\frac{20}{\sqrt{2}}\text{cm/s}$
3. $\frac{10}{\sqrt{2}}\text{cm/s}$
4. $10\text{cm/s}$

Q. Two blocks are connected by a string, as shown in figure. They are released from rest. The coefficient of kinetic friction between the upper block and the surface is 0.5. Assume that the pulley is massless and frictionless. Their common speed after they have moved a distance $5m$ will be: ($g=10m{s}^{-2}$)

1. $10\text{m/s}$
2. $5\text{m/s}$
3. $2.5\text{m/s}$
4. $25\text{m/s}$

Q. A block of mass $m$ is hung from a pulley of mass $M$ and radius $R$ and then released from rest. Initially the block is at height $h$ from the floor. The speed of the block when it strikes the floor if $M=4m$ will be

1. $\sqrt{2gh}$
2. $\sqrt{gh}$
3. $\sqrt{\frac{2gh}{3}}$
4. $\sqrt{\frac{gh}{2}}$

Q. A small bucket of mass $Mkg$ is attached to a long inextensible massless cord of length $L$. The bucket is released from rest when the cord is in a horizontal position. At its lowest position, the bucket scoops up m kg of water and swings up to a height $h$. The height $h$ in meters is
$\frac{x}{8}{\left(\frac{M}{M+m}\right)}^{2}L$. Find $x$.

Q. A ball is thrown vertically upwards.It was observed at a height h twice with a gap of time interval Δt .Find the initial velocity of the ball in terms of g and h .

Q. The average velocity of the object over the time interval ($2s$ to $4s$) will be (here $x$ is the position of the object)

1. $2\text{m/s}$
2. $8\text{m/s}$
3. $4\text{m/s}$
4. $6\text{m/s}$

Q. a block resting on rough horizontal surface a sharp horizontal impulse is given on block at t=0 the graph between velocity and displacement for motion of block is

Q. A train of length $100\text{m}$ is crossing a bridge $200\text{m}$ long in length at the speed of $72\text{kmph}$. What is the time taken by the train to cross the bridge?

1. 5 seconds
2. 10 seconds
3. 15 seconds
4. 20 seconds

Q. Two boys are standing at the ends A and B of a ground, where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity $v_1$. The boy at A starts running simultaneously with velocity $v$ and catches the other boy in a time t, where t is

1. $\frac{a}{\sqrt{v^2+v_1^2}}$
2. $\frac{a}{(v-v_1)}$
3. $\sqrt{\frac{a^2}{v^2-v_1^2}}$
4. $\frac{a}{(v+v_1)}$

Q. The pulley shown in the figure has radius $20\text{cm}$ and moment of inertia $0.2{\text{kg m}}^2$. Spring used has force constant $50{\text{N m}}^{-1}$. The system is released from rest. Find the velocity of $1\text{kg}$ block when it has descended $10\text{cm}$

1. $\frac{1}{2}{\text{ms}}^{-1}$
2. $\frac{1}{\sqrt{2}}{\text{ms}}^{-1}$
3. $\frac{1}{\sqrt{3}}{\text{ms}}^{-1}$
4. None

Q. A particle is projected making an angle of ${45}^{\circ }$ with horizontal, with kinetic energy $K$. The kinetic energy at highest point will be

1. $\frac{K}{\sqrt{2}}$
2. $\frac{K}{2}$
3. $2K$
4. $K$

Q. The motion of a particle along a straight line is described by the function $x=6+4t^2–t^4$ where $x$ is in meters and $t$ is in seconds. What is the maximum velocity attained by the particle ?

1. $\frac{16}{3}\sqrt{\frac{2}{3}}\text{m/s}$
2. $\frac{14}{3}\sqrt{\frac{2}{3}}\text{m/s}$
3. $\frac{14}{3}\sqrt{\frac{3}{2}}\text{m/s}$
4. $\frac{16}{3}\sqrt{\frac{3}{2}}\text{m/s}$

Q.

A body moves such that its position varies with time according to $x\left(t\right)=3t^2$. What is its velocity at=3sec?

1. 6 m/s

2. 18 m/s

3. -18 m/s

4. 27 m/s

Q. De Broglie wavelength of an electron after being accelerated by a potential difference of V volt from rest is

1. $\lambda =\frac{12.3}{\sqrt{h}}A$
2. $\lambda =\frac{12.26}{\sqrt{V}}A$
3. $\lambda =\frac{12.3}{\sqrt{E}}A$
4. $\lambda =\frac{12.3}{\sqrt{m}}A$

Q. Two boys are standing at the ends A and B of a ground where AB = a . The boy at B starts running in a direction perpendicular to AB with velocity $v_1)$_. The boy at A starts running simultaneously with velocity v and catches the other boy in a time t, where t is

1. 
2. 
3. 
4. 

Q.

An athlete completes one round of a circular track of a diameter of $200m$ in $40s$ What will be the displacement at the end of $2minutes40s$?

1. $2200m$

2. $220m$

3. $22m$

4. zero

Q. The relation between time $t$ and distance $x$ is $t=a{x}^2+bx,$ where $a$ and $b$ are constants. The acceleration is

1. $-2ab{v}^2$
2. $2b{v}^3$
3. $-2a{v}^3$
4. $2a{v}^2$