Relative Motion in 1D

Q. Two bodies $A$ and $B$ are travelling with constant velocities of $20\text{m/s}$ and $30\text{m/s}$ in the same positive direction. The relative velocity of $A$ with respect $B$ is

1. $10\text{m/s}$
2. $-10\text{m/s}$
3. $30\text{m/s}$
4. $50\text{m/s}$

Q. Two bodies $A$ and $B$ are travelling with constant velocities of $20\text{m/s}$ and $30\text{m/s}$ in opposite direction. The relative speed of $A$ with respect to $B$ is

1. $20\text{m/s}$
2. $30\text{m/s}$
3. $10\text{m/s}$
4. $50\text{m/s}$

Q. Two particles $A$ and $B$ are located at coordinates $(20,0)\text{m}$ and $(30,0)\text{m}$. Relative position of $A$ w.r.t. $B$ is

1. $10\text{m}$
2. $-10\text{m}$
3. $20\text{m}$
4. $-20\text{m}$

Q. Two balls $A$ and $B$ are thrown vertically upward with velocity $5\text{m/s}$ and $10\text{m/s}$ respectively. Find separation between them after one second.
(Take $g=10{\text{m/s}}^2$)

1. $10\text{m}$
2. $0\text{m}$
3. $15\text{m}$
4. $5\text{m}$

Q. A particle $A$ is moving with a speed $10\text{m/s}$ towards right while particle $B$ is moving at a speed of $10\text{m/s}$ towards right and another particle $C$ is moving at speed of $10\text{m/s}$ towards left. The separation between $A$ and $B$ is $100\text{m}$. Find the time interval between $C$ meeting $B$ and $C$ meeting $A$.

1. $5\text{s}$
2. $10\text{s}$
3. $20\text{s}$
4. C will never cross A.

Q. A motorbike is being chased by a car. The motorbike moves with the speed of $10m/s$ and has acceleration of $5m/s^2$. Whereas, the car has speed of $20m/s$ and accelerates with $3m/s^2$. If the initial separation between motorbike and car is $60m$, find the distance by which car will miss the motorbike.

1. $25m$
2. $40m$
3. $30m$
4. $35m$

Q. A motorbike is being chased by a car. The motorbike moves with the speed of $20m/s$ and has acceleration of $5m/s^2$. Whereas, the car has speed of $30m/s$ and accelerates with $3m/s^2$. If the initial separation between motorbike and car is $80m$, find the distance by which car will miss the motorbike.

1. $55m$
2. $35m$
3. $40m$
4. $30m$

Q. A boy throws a ball upwards with a velocity of $5\text{m/s}$ from a balloon descending with a constant velocity of $15\text{m/s}$. After how much time will the boy be able to catch the ball? Take $g=10{\text{m/s}}^2$ .

1. $20\text{s}$
2. $15\text{s}$
3. $4\text{s}$
4. $5\text{s}$

Q.

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

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