Velocity in 2D

Q. Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time $t_1$. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time $t_2$. The time taken by her walk up on the moving escalator will be

1. $t_1-t_2$
2. $\frac{t_1+t_2}{2}$
3. $\frac{t_1{t}_2}{t_2-t_1}$
4. $\frac{t_1{t}_2}{t_1+t_2}$

Q. A circular disc with a groove along its diameter is placed horizontally. A block of mass $1\text{kg}$ is placed as shown. The coefficient of friction between the block and all surfaces of groove in contact is $\mu =\frac{2}{5}$. The disc has an acceleration of $25\text{m}/s^2$ Find the acceleration of the block with respect to disc.

1. $10\text{m}/s^2$
2. $20\text{m}/s^2$
3. $15\text{m}/s^2$
4. $5\text{m}/s^2$

Q. The point $A$ moves with a uniform speed along the circumference of a circle of radius $0.36\text{m}$ and cover ${30}^{\circ }$ in $0.1\text{s}$. The perpendicular projection ${}^{\prime }{P}^{\prime }$ from ${}^{\prime }{A}^{\prime }$ on the diameter $MN$ represents the simple harmonic motion of ${}^{\prime }{P}^{\prime }$. The restoring force per unit mass when $P$ touches $M$ will be:

1. $100\text{N}$
2. $50\text{N}$
3. $9.87\text{N}$
4. $0.49\text{N}$

Q. A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time $t_1$. If he remains stationary on a moving escalator, then the escalator takes him up in time $t_2$. The time taken by him to walk up on the moving escalator will be:

1. $\frac{t_1{t}_2}{t_2-t_1}$
2. $\frac{t_1+t_2}{2}$
3. $\frac{t_1{t}_2}{t_2+t_1}$
4. $t_2-t_1$

Q. A body covers one-third of the distance with a velocity $v_1$, the second one-third of the distance with a velocity $v_2$ and the remaining distance with a velocity $v_3$. The average velocity is

1. $\frac{v_1+v_2+v_3}{3}$
2. $\frac{3v_1{v}_2{v}_3}{v_1{v}_2+v_2{v}_3+v_3{v}_1}$
3. $\frac{v_1{v}_2+v_2{v}_3+v_3{v}_1}{3}$
4. $\frac{v_1{v}_2{v}_3}{3}$

Q. A ball is thrown up with a certain velocity so that it reaches a height ${}^{\prime }{h}^{\prime }$. Find the ratio of the two different times of the ball reaching $\frac{h}{3}$ in both the directions.

1. $\frac{\sqrt{2}-1}{\sqrt{2}+1}$
2. $\frac{1}{3}$
3. $\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$
4. $\frac{\sqrt{3}-1}{\sqrt{3}+1}$

Q. Which of the following velocity time graphs shows a realistic situation for a body in motion?

1. 
2. 
3. 
4. 

Q. A small disc $A$ slides down with initial velocity equal to zero from the top of a smooth hill of height $H$ having a horizontal portion. What must be the height of the horizontal portion $h$ to ensure the maximum distance $s$ covered by the disc?

1. 
   $\frac{H}{2}$
2. 
   
   $\frac{H}{3}$
3. 
   
   $\frac{2H}{3}$
4. 
   $\frac{H}{4}$

Q. A particle is moving with a uniform speed $v$ in a circular path of radius $r$ with the centre at $O$. When the particle moves from a point $P$ to $Q$ on the circle such that $\angle POQ=\theta$, then the magnitude of the change in velocity is

1. $2v\sin \left(2\theta \right)$
2. zero
3. $2v\sin \left(\theta /2\right)$
4. $2v\cos \left(\theta /2\right)$

Q. A rocket is projected straight up and explodes into three equally massive fragments just as it reaches the top of its flight. One of the fragments is observed to come straight down in a time $t_1$, while the other two land together at a time $t_2$, after the burst. If the initial velocity of first segment is
$v_1=\frac{g(t_2^2-t_1^2)}{n{t}_1+t_2}$, find $n$.

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

Q.

A boat moves along the river flow from point A to B and returns back with the same speed. Speed of boat is $N$ times the speed of water. If the speed of water is $1m/s$, then the average speed of the boat (in m/s) is

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

Q. A particle moves half the time of its journey with velocity $u$. The rest of the half time it moves with two velocities $V_1$ and $V_2$ such that half the distance it covers with $V_1$ and the other half with $V_2$. Find the net average velocity. Assume straight line motion.

1. $\frac{u(V_1+V_2)+2V_1{V}_2}{2(V_1+V_2)}$
2. $\frac{2u(V_1+V_2)}{2u+V_1+V_2}$
3. $\frac{u(V_1+V_2)}{2V_1}$
4. $\frac{2V_1{V}_2}{u+V_1+V_2}$

Q. In a gravity free room a man of mass $m_1$ is standing at a height $h$ above the floor. He throws a ball of mass $m_2$ vertically downwards with a speed $u$. Find the distance of the man from the floor when the ball reaches the ground.

1. $\left(\frac{m_1+m_2}{m_1-m_2}\right)h$
2. $\frac{h}{m_1}$
3. $\frac{m_2}{m_1}h$
4. $(1+\frac{m_2}{m_1})h$

Q. Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time $t_1$. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time $t_2$. The time taken by her to walk up on the moving escalator will be

1. $\frac{t_1{t}_2}{t_2-t_1}$
2. $\frac{t_1{t}_2}{t_2+t_1}$
3. $\frac{t_1+t_2}{2}$
4. $t_1-t_2$

Q. The seconds hand of a watch has length $6\text{cm}$. Speed of end point and magnitude of difference of velocities at two perpendicular positions will be

1. $2\pi$ and $0\text{mm/s}$
2. $2\sqrt{2}\pi$ and $2\pi \text{mm/s}$
3. $2\pi$ and $2\sqrt{2}\pi \text{mm/s}$
4. $2\sqrt{2}\pi$ and $4.44\text{mm/s}$

Q. A taxi leaves the station X for station Y every 10 minutes. Simultaneously, a taxi leaves the station Y also for station X every 10 minutes. The taxis move at the same constant speed and go from X to Y or vice-versa in 2 hours. How many taxis coming from either side will each taxi meet en route from Y to X?

1. 24
2. 23
3. 12
4. 11

Q. A particle moves according to the equation $x=t^2+3t+4$ . The average velocity in the first $5\text{s}$ is

1. $6.4{\text{ms}}^{-1}$
2. $5.8{\text{ms}}^{-1}$
3. $7.6{\text{ms}}^{-1}$
4. $8{\text{ms}}^{-1}$

Q. A circular disc with a groove along its diameter is placed horizontally. A ball of mass $1\text{kg}$ is placed in it as shown. The co-efficient of friction between the ball and all surfaces of the groove in contact is $\mu =\frac{2}{5}$. The disc has an acceleration of $25{\text{m/s}}^2$. Then, the acceleration of the ball with respect to disc will be
[Take $\theta ={37}^{\circ }$ and $g=10{\text{m/s}}^2$]

1. $10{\text{m/s}}^2$
2. $12{\text{m/s}}^2$
3. $14{\text{m/s}}^2$
4. $16{\text{m/s}}^2$

Q. In a situation shown below, if the length of seconds hand is $\frac{30}{\pi }\text{cm}$, find the magnitude of change in velocity of the tip of the seconds hand.

1. $1.732\text{cm/s}$
2. $2\text{cm/s}$
3. $1.414\text{cm/s}$
4. $0\text{cm/s}$

Q.

A particle of mass $m$ is projected with a speed $u$ from the ground at angle is $\theta =\frac{\pi }{3}$ w.r.t. horizontal $x-axis$. When it has reached its maximum height, it collides completely in elastically with another particle of the same mass and velocity $u\hat{i}$. The horizontal distance covered by the combined mass before reaching the ground is:

1. $\frac{3\sqrt{3}{u}^2}{8g}$

2. $\frac{2\sqrt{2}{u}^2}{g}$

3. $\frac{5u^2}{8g}$

4. $\frac{3\sqrt{2}{u}^2}{4g}$

Q. A boy throws a ball to his friend $20\text{m}$ away. The ball reaches to the friend in $4\text{s}$. The friend then throws the ball back to boy and it reaches the boy in $5\text{s}$. Assume the ball travels with constant velocity during any throw.

1. The average velocity is $\frac{40}{9}{\text{ms}}^{-1}$
2. The average acceleration is zero.
3. The average velocity is zero but average acceleration is non-zero.
4. Average acceleration of the motion cannot be defined.

Q. A ball is projected from a horizontal surface at an angle ${60}^{\circ }$ with horizontal. The maximum height of the projectile is $240\text{m}$ from the ground. Upon hitting the ground for the first time, it loses $75\%$ of its kinetic energy. Immediately after the bounce, the velocity of the ball makes angle of ${45}^{\circ }$ with the horizontal surface. The maximum height of the ball after the bounce is

1. $60\text{m}$
2. $120\text{m}$
3. $240\text{m}$
4. $180\text{m}$

Q. Which of the following velocity-time graphs shows a realistic situation for a body in motion?

1. 
2. 
3. 
4. 

Q. A boat covers a certain distance between two spots in a river taking $t_1$ hrs going downstream and $t_2$ hrs going upstream. What time will be taken by boat to cover same distance in still water ?

1. $\frac{t_1+t_2}{2}$
2. $2(t_2=t_1)$
3. $\frac{2t_1{t}_2}{t_1+t_2}$
4. $\sqrt{t_1{t}_2}$

Q. In a gravity free room a man of mass $m_1$ is standing at a height $h$ above the floor. He throws a ball of mass $m_2$ vertically downwards with a speed $u$. Find the distance of the man from the floor when the ball reaches the ground.
(Neglect the height of the man)

1. $\left(\frac{m_1+m_2}{m_1-m_2}\right)h$
2. $\frac{h}{m_1}$
3. $(1+\frac{m_2}{m_1})h$
4. $\frac{m_2}{m_1}h$

Q.

The rectangular pupil of an octopus is estimated to be $20$ millimetres long with an area of $(20x-200)$square millimetres. Write an expression that represents the perimeter (in millimetres) of the octopus pupil.

Q. A person traveling on a straight line moves with a uniform velocity $v_1$ for a distance $x$ and with uniform velocity $v_2$ for the next equal time. The average velocity $v$ is given by

1. $v=\frac{v_1+v_2}{2}$
2. $v=\sqrt{v_1{v}_2}$
3. $v=\frac{v_1{v}_2}{v_1+v_2}$
4. $v=\frac{v_1+v_2}{v_1{v}_2}$

Q. A car is moving with speed $30m/sec$ on a circular path of radius $500m$. Its speed is increasing at the rate of $2m/se{c}^2$. What is the net acceleration of the car at that moment (i.e the vector sum of tangential and radial acceleration)?

Q. Two waves having the same wavelength and amplitude but having a constant phase difference with time are known as :

1. identical waves
2. incoherent waves
3. coherent waves
4. collateral waves

Q. A circular disc with a groove along its diameter is placed horizontally. A block of mass $1\text{kg}$ is placed as shown. The coefficient of friction between the block and all surfaces of groove in contact is $\mu =\frac{2}{5}$. The disc has an acceleration of $25\text{m}/s^2$ Find the acceleration of the block with respect to disc.

1. $10\text{m}/s^2$
2. $20\text{m}/s^2$
3. $15\text{m}/s^2$
4. $5\text{m}/s^2$