Relative Motion in 1D

Q.

A car accelerates uniformly from 18 km/h to 36 km/h in 5 seconds. Calculate (i) the acceleration and (ii) the distance covered by the car in that time.

Q. WHAT IS REST

Q.

A person walks up a stationary escalator in the time $t_1$. If he remains stationary on the escalator, then it can take him up in time $t_2$. Determine the time it would take to walk upon the moving escalator ?

1. $\begin{array}{l}\frac{t_1{t}_2}{t_1+t_2}\end{array}$

2. $\begin{array}{l}\frac{t_1{t}_2}{t_1-t_2}\end{array}$

3. $\begin{array}{l}\frac{2t_1{t}_2}{t_1+t_2}\end{array}$

4. $\begin{array}{l}\frac{2t_1{t}_2}{t_1-t_2}\end{array}$

Q. A car travels the first half distance with constant velocity of $40kmph$ and the remaining half with a constant velocity of $60kmph$. The average velocity of the car in $kmph$ is

1. $40$
2. $48$
3. $50$
4. $45$

Q.

What is the numerical ratio of velocity to speed of an object?

Q. From point $A$ located on a highway, one has to get as soon as possible, by a car, to point $B$ located in a field off the highway, at a distance $l$ from point $D$. If the car moves $n$ times slower in the field, at what distance $x$ from $D$ must one turn off the highway?

1. $\frac{2l}{\sqrt{n^2-1}}$
2. $\frac{l}{\sqrt{n^2-1}}$
3. $\frac{l}{\sqrt{n-1}}$
4. $\frac{l}{\sqrt{n}}$

Q. The velocity of kerosene oil in a horizontal pipe is 5 m/s. If $g=10m/s^2$then the velocity head of oil will be

1. 1.25 m
2. 0.125 m
3. 12.5 m
4. 125 m

Q.

Two cars $\mathrm{A}$ and $\mathrm{B}$ are moving with the same speed of $45\mathrm{km}/\mathrm{h}$ along the same direction. If a third car $\mathrm{C}$ comes from the opposite direction with a speed of $36\mathrm{km}/\mathrm{h}$ meets two cars in an interval of $5\min$, the distance of separation of two cars $\mathrm{A}$ and $\mathrm{B}$ should be (in km).

1. $6.75km$

2. $7.25km$

3. $5.55km$

4. $8.35km$

5. $4.75km$

Q. Two cars A and B Are moving in same direction with velocities 30 m/s and 20 m/s.When car A is at a distance d behined tha car B , the driver of tha car A applies brakes producing uniform retardation of 2 m/s2. Find d

Q.

A train is running at a speed of$40km/hr$ and it crosses a post in$18seconds$. What is the length of the train?

1. $190metres$

2. $160metres$

3. $200metres$

4. $120metres$

Q.

$A$ moves with $65km/h$ while $B$ is coming back of $A$ with $80km/h$. The relative velocity of $B$ with respect to $A$ is

1. $80km/h$

2. $60km/h$

3. $15km/h$

4. $145km/h$

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.

A body falls freely for 10 sec. It's avg velocity during this journey is? ( g= 10 m per s square)

Q. Scooter moving with constant acceleration covers the distance between two points in 6 seconds its speed when it passes the second point is 15 metre per second what will be its velocity when it passes from first point. If the distance between the two point is 60 m

Q. When two bodies are moving in opposite directions along a straight path then the relative velocity of each body is greater than the absolute velocity of either body.
let the velocity of A and B moving in opposite directions be Va and Vb respectively.
Va=+V , Vb=-V
Velocity of B with respect to A
​​​​​​Vb - Va = -V-V= -2V which is not greater than the absolute velocity of B i.e, V
please explain this case.
​​​​​​
​​​​​​

Q. A hammer of mass $2.5kg$ moving with a speed of $1m/s$ strikes ahead of a nail driving it $10cm$ into the wall. Find the impulse applied by nail on the hammer

1. $1.5N$
2. $2.5N$
3. $5N$
4. $3.5N$

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.

One car is at rest and velocity of light from head light is c, then velocity of light from the headlight of moving car at velocity v, would be?

Q.

What is the main concept of relative velocity?

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. PSLV launches a rocket in a gravity free space with constant acceleration $5{\text{m/s}}^2$ along +x direction (see figure). The length of the chamber inside the rocket is $6\text{m}$. At time $t=0$, a ball is thrown from the left end of the chamber in +x direction with a speed $0.7\text{m/s}$ relative to the rocket. At the same time, another ball is thrown in opposite direction to the previous ball with a speed $0.3\text{m/s}$ relative to the rocket. The time in seconds when the two balls hit each other is

Q.

A truck travelling due north at 20m/s turns west and travels at same speed. The change in velocity be

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. The velocities of a body moving along a straight line with a constant acceleration are 10m/s at t=4s and 20m/s at t=9s. The velocity of athe body at t=1s is

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. 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. Ship $\text{A}$ is sailing towards north-east with velocity vector $\overrightarrow{v}=30\hat{i}+50\hat{j}\text{km/hr}$ where $\hat{i}$ points east and $\hat{j}$ north. Ship $B$ is at a distance of $80\text{km}$ east and $150\text{km}$ north of Ship $A$ and is sailing towards west at $10\text{km/hr}$. $A$ will be at minimum distance from $B$ in,

1. $2.2\text{hrs}$
2. $4.2\text{hrs}$
3. $2.6\text{hrs}$
4. $3.2\text{hrs}$

Q.

Ship moving with velocity${\overrightarrow{V}}_1=30\stackrel{⏜}{i}+50\stackrel{⏜}{j}$ from position $(0,0)$ and ship B moving with velocity ${\overrightarrow{V}}_2=-10\stackrel{⏜}{i}$ from position $(80,150)$. The time for minimum separation is

1. $2.6$

2. $2.2$

3. $2.4$

4. None of these

Q.

A body travelling along a straight line transversed one third of the total distance with a velocity 4 m/s . The remaining part of the distance was covered with a velocity 2 m/s for half time and with velocity 6 m/s for the other half of time . The mean velocity averaged over the whole time of motion is