Relative Position

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. $25\text{m}$ from ground
4. $20\text{m}$ from ground

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

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 bus starts moving with acceleration $2{\text{ms}}^{-2}$. A cyclist $96\text{m}$ behind the bus starts simultaneously toward the bus at a constant speed of $20\text{m/s}$. After some time, the bus will be left behind. If the bus continues moving with the same acceleration, after what time from the beginning, the bus will overtake the cyclist?

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

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

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

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. A stone is allowed to fall from the top of a tower $100\text{m}$ high and at the same time, another stone is projected vertically upwards from the ground with a velocity of $25{\text{ms}}^{-1}$. The two stones will meet after

1. $4\text{s}$
2. $0.4\text{s}$
3. $0.04\text{s}$
4. $40\text{s}$

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

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

Q.

Two bodies move towards each other from 10 m apart with a constant velocity they meet at C after 2s. What is the displacement of B w.r.t. A?

1. -6 m

2. 10 m

3. -10 m

4. 6 m

Q. A bus starts moving with acceleration $2{\text{ms}}^{-2}$. A cyclist $96\text{m}$ behind the bus starts simultaneously toward the bus at a constant speed of $20\text{m/s}$. After some time, the bus will be left behind. If the bus continues moving with the same acceleration, after what time from the beginning, the bus will overtake the cyclist?

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

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. 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. In a bicycle competition called Tour De France, two riders; $A$ and $B$ are riding bicycles at constant acceleration of magnitude $1{\text{m/s}}^2$ and $3{\text{m/s}}^2$ respectively, in the North direction. Their initial speeds are $15\text{m/s}$ and $10\text{m/s}$ respectively while they were heading in the North direction. Find the separation between them after $t=10\text{s}$.

1. $80\text{m}$
2. $95\text{m}$
3. $50\text{m}$
4. $125\text{m}$

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

Q. One body is dropped, while a second body is thrown downward with an initial velocity of $1{\text{ms}}^{-1}$ simultaneously. After what time separation between the two bodies is $18\text{m}$?

1. $4.5\text{s}$
2. $9\text{s}$
3. $18\text{s}$
4. $36\text{s}$

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

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