Relative Acceleration

Q.

At the instant the traffic light turns green, an automobile starts with a constant acceleration, $a=10m/s^2.$ At the same instant a truck, travelling with a constant speed of 5 m/s, overtakes and passes the automobile. (a) How far beyond the traffic signal will the automobile overtake the truck? (b) How fast will the automobile be at that instant?

1. 10m, 15 m/s

2. 5m, 10 m/s

3. 10m, 10 m/s

4. 5m, 15 m/s

Q.

At the instant the traffic light turns green, an automobile starts with a constant acceleration, $a=10m/s^2.$ At the same instant a truck, travelling with a constant speed of 5 m/s, overtakes and passes the automobile. (a) How far beyond the traffic signal will the automobile overtake the truck? (b) How fast will the automobile be at that instant?

1. 10m, 15 m/s

2. 5m, 10 m/s

3. 10m, 10 m/s

4. 5m, 15 m/s

Q. A boy stands at a distance 'd' behind the bus. The bus and boy start moving simultaneously; the boy with an initial and constant velocity of 'v' and the bus starts from rest with an acceleration of 'a' What is the minimum value of 'v' such that the boy successfully catches the bus?

1. $\sqrt{2ad}$
2. $\sqrt{ad}$
3. $\sqrt{ad/2}$
4. infinite

Q. An elevator car, whose floor to ceiling distance is equal to 2.7 m, starts ascending with constant acceleration of 1.2 $m{s}^{-2}$. 2 sec after the start, a bolt begins fallings from the ceiling of the car. The free fall time of the bolt is

1. $\sqrt{0.54}$ s
2. $\sqrt{6}$ s
3. $\sqrt{0.7}$ s
4. $1s$

Q.

I want to play a prank on my friend and turn his world upside down, at what acceleration must his lift move to make it seem that the world is upside down to him

1. g downwards

2. g upwards

3. 2g downwards

4. 2g upwards

Q.

A ball is thrown up with a speed of $9.8m{s}^{-1}$. What is the time taken by the ball to reach back to the starting point from the highest point reached?

Q. Hey, try to solve this question using relative motion concepts now; by moving to the frame of the bus.
A boy stands at a distance 'd' behind the bus. The bus and boy start moving simultaneously; the boy with an initial and constant velocity of 'v' and the bus starts from rest with an acceleration of 'a' What is the minimum value of 'v' such that the boy successfully catches the bus?

1. $\sqrt{2ad}$
2. $\sqrt{ad}$
3. $\sqrt{ad/2}$
4. infinite

Q. A swimmer jumps upwards from a diving board( A) and while she is going up another swimmer just walks off the diving board(B). Then throughout time of flight swimmer B will see swimmer A

1. going up and coming down with acceleration g

2. going up for a while with a constant velocity and then coming down with a constant velocity

3. going up but with an acceleration downwards of g

4. going only up with a constant velocity

Q.

A man in a balloon throws a stone downwards with a speed of 5 m/s with respect to balloon. The balloon is moving upwards with a constant acceleration of $5m/s^2$Then velocity of the stone relative to the man after 2 second is

1. 10 m/s

2. 30 m/s

3. 15 m/s

4. 35 m/s

Q. Two bodies $A$ and $B$ are thrown simultaneously. $A$ is projected vertically upwards with $80\text{m/s}$ speed from the ground and $B$ is projected vertically downwards from a height of $160\text{m}$ with $40\text{m/s}$ and along the same line of motion. The time taken for the two bodies to collide is

1. $1\text{sec}$
2. $1.33\text{sec}$
3. $1.66\text{sec}$
4. $2\text{sec}$

Q.

On a two-lane road, car A is travelling with a speed of 36 km/hr. Two cars, B and C approach car A in opposite directions with a speed of 54 km/h. At a certain instant, when the distance AB is equal to AC, both 1 km, B decided to overtake A before C does. What minimum acceleration of car B is required to avoid an accident.

1. $10m/s^2$

2. $2m/s^2$

3. $0m/s^2$

4. $1m/s^2$

Q. Lift A is going up with velocity 20m/s and acceleration as $8m/s^2$ in the downward direction. While lift B is going down with 10m/s and acceleration of $+2m/s^2$ in upward direction. At this moment a bolt in the ceiling of lift A gets loose and falls. Height of the lift is 16 m.

What is the velocity of bolt relative to lift B when it hits the floor of A.?

1. 18 m/s

2. 20 m/s

3. 22 m/s

4. None of these

Q. An elevator which is moving with an upward acceleration of "a $m/s^2$”. A person drops a coin to measure the acceleration 'a $m/s^2$'. Find 'a' if the coin took 0.5s to hit the ground and the coin was dropped from a height of 3 m.

1. $10m/s^2$
2. $14m/s^2$
3. $5m/s^2$
4. $0m/s^2$

Q.

A particle is thrown up with velocity $v_0$ inside a stationary lift of sufficient height. The time of flight is 'T'. Now it is thrown again with same initial speed $v_0$ with respect to lift. If at the time of second thrown, lift is moving up with a velocity $v_0$ and uniform acceleration g upward. Which of the following are true?

1. (a)Displacement-time graph of particle when lift was stationary

   

2. (b)Displacement-time graph of the particle with respect to the moving lift.

   

3. (c)Displacement-time graph of the particle with respect to ground when the lift is moving

   

4. (d) Velocity-time graph of the particle with respect to the moving lift.

   

Q.

Two cars 1 and 2 move with velocities $v_{1}and{v}_2$ respectively on a straight road in the same direction. When the cars are separated by a distance d, the driver of the car 1 applies brakes and the car moves with uniform retardation $a_1$. Simultaneously, the car 2 starts accelerating with $a_2$. If $v_1>v_2$, find the minimum initial separation between the cars to avoid collision between them.

1. $d=\frac{(v_1-v_2{)}^2}{\left(a_1{a}_2\right)}\frac{a_1}{a_2}$

2. $d=\frac{2\left(a_1{a}_2\right)}{(v_1-v_2{)}^2}$

3. $d=\frac{(v_1-v_2{)}^2(v_1)}{(a_1+a_2)v_2}$

4. $d=\frac{(v_1-v_2{)}^2}{2(a_1+a_2)}$

Q.

I cut the rope of an elevator and it begins to fall freely. A person inside (aware of his imminent doom) tries to make a last minute contribution to science by dropping a ball. Then what will he observe?

1. The ball will fall and hit the bottom but take longer than it does on the earth

2. The ball will go upwards and hit the ceiling

3. The ball will fall and take the same time it takes on the ground

4. The ball will not fall downwards or upwards but just float wherever it is.

Q.

A block of mass 2 kg is kept inside a lift. Lift starts moving downward with an acceleration of a = $12m/s^2$. Height of the lift is 4m. Time after which block will strike roof of the lift is (Take g = $10m/s^2$)

1. 2 second

2. 3.5 second

3. 4 second

4. 5.2 second

Q. An elevator is moving up with an acceleration $a{\text{m/s}}^2$. A person inside the lift throws the ball upwards with a velocity $u\text{m/s}$ relative to himself. Then the time of flight of ball ($\text{in sec}$) will be:

1. $\frac{u}{g+a}$
   
2. $\frac{u}{g-a}$
   
3. $\frac{2u}{g+a}$
   
4. $\frac{2u}{g-a}$
   

Q.

Lift A is going up with velocity 20m/s and acceleration of $8m/s^2$ in the downward direction. While lift B is going down with 10m/s and acceleration of $+2m/s^2$ in upward direction. At this moment a bolt in the ceiling of lift A gets loose and falls. Height of the lift is 16 m.Find the displacement of bolt relative to B when it hits the floor of A.

1. 20 m

2. 24 m

3. 32 m

4. 36 m

Q.

A man in a balloon throws a stone downwards with a speed of 5 m/s with respect to balloon. The balloon is moving upwards with a constant acceleration of $5m/s^2$Then velocity of the stone relative to the man after 2 second is

1. 10 m/s

2. 30 m/s

3. 15 m/s

4. 35 m/s

Q. A car and a truck move in the same straight line at the same instant of time from the same place. The car moves with a constant velocity of $40m/s$ and the truck starts with a constant acceleration of $4m/s^2$. Find the time $t$ that elapses before the truck catches up with the car.

1. $10s$
2. $20s$
3. $30s$
4. $40s$

Q. A hot air balloon is rising with an acceleration of 10 $m/s^2$. The moment when its velocity is 10 m/s, a stone is dropped which of the following is the displacement time graph of the stone with respect to the balloon.

1. 

2. 

3. 

4. 

Q. Two cars A and B are travelling in the same direction with velocities $v_1$ and $v_2(v_1>v_2)$ When the car A is at a distance d ahead of the car B, the driver of the car A applied the brake producing a uniform retardation a. There will be no collision when

1. $d<\frac{(v_1-v_2{)}^2}{2a}$
2. $d<\frac{(v_1^2-v_2^2)}{2a}$
3. $d>\frac{(v_1-v_2{)}^2}{2a}$
4. $d>\frac{(v_1^2-v_2^2)}{2a}$