Relative Position

Q.

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

1. 10 m

2. -4 m

3. 4 m

4. -10 m

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. 10 m

2. -10 m

3. 6 m

4. -6 m

Q. Two stones are thrown up simultaneously with initial speeds of $u_1$ and $u_2(u_2>u_1)$. They hit the ground after $6\text{s}$ and $10\text{s}$ respectively. Which graph in figure correctly represents the time variation of $\Delta x=(x_2-x_1)$, the relative position of the second stone with respect to the first upto $t=10\text{s}$?
Assume that the stones do not rebound after hitting the ground.

1. 
2. 
3. 
4. 

Q. The graph shown illustrates velocity versus time for two cars $A$ and $B$ constrained to move in a straight line. Both cars were at the same position at $t=0\text{s}$. Consider the following statements.
(1) Car $A$ is travelling west, and Car $B$ is travelling east.
(2) Car $A$ overtakes Car $B$ at $t=5\text{s}$
(3) Car $A$ overtakes Car $B$ at $t=10\text{s}$ .

Which of the following is correct?

1. Only statement 1 and 2 are true
2. Only statement 1 is true
3. Only statement 2 is true
4. Only statement 3 is true

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. 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 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. 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 lift starts moving up with an acceleration of $5{\text{ms}}^{-2}$, and at the same instant a ball is dropped from a height of $1.25\text{m}$. The time taken by the ball to reach the floor of the lift is (nearly)
$(g=10{\text{ms}}^{-2})$

1. $0.3$ second
2. $0.2$ second
3. $0.16$ second
4. $0.4$ second