Relative Position

Q. Two cars start off to race with velocities $4\text{m/s}$ and $2\text{m/s}$ and travel in a straight line with uniform accelerations $1{\text{m/s}}^2$ and $2{\text{m/s}}^2$ respectively. If they reach the final point at the same time instant, then what is the length of the path?

1. $12\text{m}$
2. $18\text{m}$
3. $24\text{m}$
4. $30\text{m}$

Q. A man is $25\text{m}$ behind a bus, when the bus starts accelerating at $2{\text{m/s}}^2$ and man starts moving with constant velocity of $10\text{m/s}$. Time taken by him to board the bus is

1. $2\text{s}$
2. $3\text{s}$
3. $4\text{s}$
4. $5\text{s}$

Q.

An artificial satellite is moving around earth in a circular orbit with speed equal to one fourth the escape speed of a body. From the surface of earth the hight of satellite above earth's surface is (R = radius of earth)

Q. A ball is dropped from the top of a building $100\text{m}$ high. At the same instant another ball is thrown upwards with a velocity of $40{\text{ms}}^{-1}$ from the bottom of the building. The two balls will meet after

1. $5\text{s}$
2. $2.5\text{s}$
3. $2\text{s}$
4. $3\text{s}$

Q.

A particle starts its motion from rest under the action of a constant force.if the distance covered in first 10 sec is S1 and that covered in the first 20 sec is S2 , then

a. S2=2S1

b. S2=3S1

c. S2=4S1

d. S2=S1

Q.

Is absolute rest and absolute motion possible ?

Q.

A lift is moving down with acceleration $a$. A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively

1. $g,g$

2. $g–a,g–a$

3. $g–a,g$

4. $a,g$

Q. Two bodies $A$ and $B$ are thrown simultaneously. $A$ is projected vertically upwards with $20\text{m/s}$ speed from the ground and $B$ is projected vertically downwards from a height of $40\text{m}$ at the same speed and along the same line of motion. At what point do the two bodies collide?
$(g=10{\text{m/s}}^2)$

1. $10\text{m}$ from ground
2. $15\text{m}$ from ground
3. $20\text{m}$ from ground
4. $25\text{m}$ from ground

Q.

A thief is running away on a straight road on a jeep moving with a speed of $9\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$. A police man chases him on a motor cycle moving at a speed of $10\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$. If the instantaneous separation of jeep from the motor cycle is $100m$, how long will it take for the policemen to catch the thief ?

1. $1sec$

2. $19sec$

3. $90sec$

4. $100sec$

Q. A body is at rest at $x=0$. At $t=0$, it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through $x=0$ moving in the positive x-direction with a constant speed. The position of the first body is given by $x_1\left(t\right)$ after time $t$ and that of the second body by $x_2\left(t\right)$ after the same time interval. Which of the following graphs correctly describes $(x_1-x_2)$ as a function of time $t$?

1. 
2. 
3. 
4. 

Q. A block slides down a smooth inclined plane when released from the top, while another falls freely from the same point. Which one of them will strike the ground: (a) earlier (b) with greater speed?

Q. Two balls are projected upward simultaneously with speeds $40\text{m/s}$ and $60\text{m/s}$. Relative position $\left(x\right)$ of second ball w.r.t. first ball at time $t=5\text{s}$ is :
[Neglect air resistance]

1. $20\text{m}$
2. $80\text{m}$
3. $100\text{m}$
4. $120\text{m}$

Q. A stone $A$ is dropped from rest from height $h$ above the ground. A second stone $B$ is simultaneously thrown vertically up from a point on the ground with velocity $v$. Find $v$ so that $B$ meets $A$ midway between their initial positions.

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

Q. The position of an object changes from r=(2i + j)m to r1=(4i + 3j)m in 2 sec .Find its average velocity?

Q. A man is standing in a lift moving upwards with a constant speed of $10{\text{ms}}^{-1}$. The man drops a coin from a height of $4.9\text{m}$. If $g=9.8{\text{ms}}^{-2}$, the coin reaches the floor of the lift after a time

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

Q. Two particles, one with constant velocity $50{\text{ms}}^{-1}$ and the other with uniform acceleration $10{\text{ms}}^{-2}$, start moving simultaneously from the same place in the same direction. When will the accelerated particle be $125\text{m}$ ahead of the other particle?

1. $5(1+\sqrt{2})\text{s}$
2. $10\text{s}$
3. $10(\sqrt{2}+1)\text{s}$
4. $3\text{s}$

Q.

The states of rest and motion are ____________.

Q. A man is $d$ distance behind a bus. The bus starts moving away from the man with an acceleration $a$. At the same time man starts running towards the bus with a constant velocity $v$.

1. The man catches the bus if $v\ge \sqrt{2ad}$
2. If man just catches the bus, the time of catching the bus will be $t=\frac{v}{a}$
3. If man just catches the bus, the time of catching the bus will be $t=\frac{2v}{a}$
4. The man will catch the bus if $v\le \sqrt{ad}$

Q.

Write the equations of motion when an object falling freely towards earth or thrown vertically upwards.

Q. A car is moving with a uniform speed on a level road. Inside the car there is a balloon filled with helium and attached to a piece of string tied to the floor. The string is observed to be vertical. The car now takes a left turn maintaining the speed on the level road. The balloon in the car will

1. Burst while taking the curve
2. Be thrown to the right side
3. Be thrown to the left side
4. Continue to remain vertical

Q.

A train is moving with a velocity of $20\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$ on this, dust is falling at the rate of $50\raisebox{1ex}{$kg$}\!\left/ \!\raisebox{-1ex}{$min$}\right.$. The extra force required to move this train with a constant velocity will be

1. $16.66N$

2. $1200N$

3. $1000N$

4. $166.6N$

Q.

A shell of mass $10kg$ is moving with a velocity of $10m{s}^{-1}$ when it blasts and forms two parts of mass $9kg$ and $1kg$ respectively. If the first mass is stationary, the velocity of the second is

1. $1m{s}^{-1}$

2. $10m{s}^{-1}$

3. $100m{s}^{-1}$

4. $1000m{s}^{-1}$

Q. A situation is shown in which two objects $A$ and $B$ start their motion from same point in same direction. The graph of their velocities against time is drawn. $u_A$ and $u_B$ are the initial velocities of $A$ and $B$ respectively. $T$ is the time at which their velocities become equal after start of motion.

If the value of $T$ is $4\text{s}$, then the time after which $A$ will meet $B$ is

1. $6\text{s}$
2. $8\text{s}$
3. data insufficient
4. $12\text{s}$

Q. Two particles, one with constant velocity of $50{\text{ms}}^{-1}$ and the other with uniform acceleration $10{\text{ms}}^{-2}$, start moving simultaneously from the same place in the same direction. When will the accelerated particle be $125\text{m}$ ahead of the other particle?

1. $3\text{s}$
2. $5(1+\sqrt{2})\text{s}$
3. $10\text{s}$
4. $10(\sqrt{2}+1)\text{s}$

Q. On a foggy day, two drivers spot in front of each other when 18 apart. they were travelling at 70 km per hour and 60 km per hour. Both apply brakes simultaneously which retard the cars @5 m per second square. Which of the following statement is correct and also give reasons a) the collision will be averted b) the collision will take place c) they will cross each other d) they will just collide

Q. A cricket ball of mass 100g moving with a velocity of 20m/s is brought to rest by a player in 0.05s the impulse of the ball is

Q. For the figure given below, find the value of $x_{BA},x_{CA},x_{CB},x_{AB}$ and $x_{AC}$ respectively where $x_{AB}$ represents position of $A$ with respect to $B$.

1. $4\text{m},10\text{m},6\text{m},-4\text{m},-10\text{m}$
2. $4\text{m},10\text{m},-6\text{m},4\text{m},-10\text{m}$
3. $-4\text{m},10\text{m},6\text{m},-4\text{m},-10\text{m}$
4. $4\text{m},-10\text{m},6\text{m},-4\text{m},10\text{m}$

Q.

Can a body be both at rest as well as in motion? Explain.

Q. A man is walking on a road with a velocity $3km/h$. Suddenly rain starts falling. Velocity of rain is $10km/h$ in vertically downward direction. The relative velocity of the rain with respect to man is

1. $\sqrt{13}km/hr$
2. $\sqrt{7}km/hr$
3. $\sqrt{109}km/hr$
4. $13km/hr$

Q.

The distance between New Orleans and Houston is $353$ miles.

At $12:20\mathrm{PM}$, a bus leaves Houston for New Orleans at a speed of $60\mathrm{mph}$.

Forty-five minutes later, a motorcycle leaves New Orleans for Houston at a speed of $72\mathrm{mph}$.

At what time will the bus and the motorcycle pass each other if neither stops nor changes speed?