Distance vs Displacement

Q.

An insect crawls up $5\mathrm{cm}$ every second on a $60\mathrm{cm}$ vertical rod and then falls down $2\mathrm{cm}$ over the next second . How many seconds will it take to climb the rod?

Q.

How does instantaneous velocity differ from average velocity?

Q. The magnitude of displacement can be zero even when the distance is non zero.

1. False
2. True

Q. A particle moves from A to B along the semicircular curve as shown in the figure. The ratio of distance covered by particle to its displacement is

1. $\frac{\pi }{2}$
2. $\frac{2}{\pi }$
3. $\frac{\pi }{4}$
4. $1:1$

Q. John travels $250\text{m}$ to North but then back-tracks to South for $100\text{m}$ to pick up a friend. What is John’s total displacement?

1. $100\text{m}$
2. $150\text{m}$
3. $50\text{m}$
4. $250\text{m}$

Q. The location of a particle is changed. What can we say about the displacement and distance covered by the particle?

1. Both cannot be zero
2. One of the two may be zero
3. Both must be zero
4. Both must be equal

Q. A ball is thrown upwards, which attains a height of $10\text{m}$ and comes back to the same position.
$i$ What is the net distance?
$ii$ What is the net displacement?

1. $i.10\text{m},ii.0$
2. $i.20\text{m},ii.0$
3. $i.10\text{m},ii.10\text{m}$
4. $i.20\text{m},ii.20\text{m}$

Q. The numerical ratio of displacement to distace for moving object is

1. always less than $1$
2. always equal to $1$
3. always more than $1$
4. equal or less than $1$

Q.

An ant moves from A to B. Find the distance (d) and displacement ( s).

1. d = 0 cm, s = 5cm

2. d = 5 cm, s = 0 cm

3. d = 5 cm, s = 5 cm

4. d = 0 cm, s = 0 cm

Q. Consider two particles $P$ and $Q$. Particle $P$ moves from $A$ to $B$ and particle $Q$ moves from $C$ to $D$. If the displacement of particle $P$ and $Q$ be $x$, $y$ respectively. Then:

1. $x=y$
2. $x<y$
3. $x>y$
4. $x\ge y$

Q. Two friends start a race, and together they run for $50\text{m}$. Rohan turns right and runs $60\text{m}$ while Rocky turns left and runs $40\text{m}$. Then Rohan turns left and runs $50\text{m}$ while Rocky turns right and runs $50\text{m}$. How far are the two friends now from each other?

1. $60\text{m}$
2. $20\text{m}$
3. $100\text{m}$
4. $50\text{m}$

Q. At $t=0$, a particle starts from $(-2,0)$ and moves towards positive $x-$axis with speed of $v=6t^2+4t\text{m/s}$. The final position of the particle and the distance travelled by the particle respectively, as a function of time are

1. $2t^3-2t^2+2\text{m},2t^3-2t^2\text{m}$
2. $2t^3+2t^2-2\text{m},2t^3+2t^2\text{m}$
3. $2t^3-2t^2-2\text{m},2t^3+2t^2\text{m}$
4. $2t^3-2t^2+2\text{m},2t^3+2t^2\text{m}$

Q. The displacement of a particle moving in a straight line is described by the relation $x\text{(in m)}=6+12t-2t^2$. The distance covered by the particle in first $5\text{s}$ is

1. $16\text{m}$
2. $10\text{m}$
3. $24\text{m}$
4. $26\text{m}$

Q. Two friends start a race, and together they run for $50\text{m}$. Rohan turns right and runs $60\text{m}$ while Rocky turns left and runs $40\text{m}$. Then Rohan turns left and runs $50\text{m}$ while Rocky turns right and runs $50\text{m}$. How far are the two friends now from each other?

1. $60\text{m}$
2. $20\text{m}$
3. $100\text{m}$
4. $50\text{m}$

Q. A person is climbing on a vertical pole of height $18\text{m}$. Starting from the height of $2\text{m}$ of the pole, if he climbs $0.5\text{m}$ in one second, how far will he be after $10\text{s}$ from the base of the pole?

1. $5\text{m}$
2. $7\text{m}$
3. $2\text{m}$
4. $8\text{m}$

Q. A person travels $100\text{km}$ in the North direction and then turns right and travels $100\text{km}$. The magnitude of displacement is

1. $200\text{km}$
2. $100\sqrt{2}\text{km}$
3. $100\sqrt{3}\text{km}$
4. None of these

Q. Suppose our school is $1\text{km}$ away from our house, and we go to school in the morning, and in the afternoon we come back. Then, the total displacement for the entire trip is

1. $1\text{km}$
2. $2\text{km}$
3. $-1\text{km}$
4. $0\text{km}$

Q. If the speed of the particle is $v=4t^3-6t^2+5\text{m/s}$, the distance of the particle as a function of time $t$ is

1. $\frac{4t^4}{3}-3t^3+5t\text{m}$
2. $t^4-2t^3+5t\text{m}$
3. $4t^4+6t^3-5t\text{m}$
4. $t^4-3t^3+5t\text{m}$

Q. A ball is thrown upwards, which attains a height of $10\text{m}$ and comes back to the same position.
$i$ What is the net distance?
$ii$ What is the net displacement?

1. $i.10\text{m},ii.0$
2. $i.20\text{m},ii.0$
3. $i.10\text{m},ii.10\text{m}$
4. $i.20\text{m},ii.20\text{m}$

Q.

In which of the following instances would the path length of travel be useful?

1. To determine how much fuel to put in the vehicle

2. To determine how long a journey might take

3. To determine the wear and tear on the vehicle

4. All of these

Q. Two particles $1$ and $2$ are moving with constant velocities ${\overrightarrow{v}}_1=4\hat{i}-3\hat{j}\text{m/s}$ and ${\overrightarrow{v}}_2=b\hat{i}-\hat{j}\text{m/s}$ respectively. The position vectors of the particles at time $t=0$ are ${\overrightarrow{r}}_1=5\hat{i}+2\hat{j}\text{m}$ and ${\overrightarrow{r}}_2=-4\hat{i}-4\hat{j}\text{m}$. If they collide, which of the following is correct. ($b$ is a constant)

1. They collide at $t=3\text{sec}$
2. Their time of collision cannot be found
3. $b=7$
4. $b=-1$

Q. Identify the incorrect statement:

1. Distance is always a positive quantity
2. Displacement may be negative
3. If displacement is zero, distance travelled by body will always be zero
4. Distance will be continously increasing for a moving body

Q.

In order to find out the amount you must change the time on your clock, which of this is sufficient?

1. The actual latitude and longitude of both the starting and the destination cities.

2. The actual longitudes alone of the starting city and the destination city.

3. Only the difference between the latitudes

4. The difference between the longitudes and the direction of travel.

Q. To determine when to change the tyre of the vehicle due to wear & tear, path length is required.

1. True
2. False

Q. A container of length $4\text{m}$, width $2\text{m}$ and height $3\text{m}$ is kept on a horizontal floor. A bee enters the container from a hole at bottom-most corner $\left(A\right)$ and comes out of the hole$\left(B\right)$ at diagonally opposite corner. If the displacement of bee is maximum when it comes out, what is its displacement ?

1. $\sqrt{20}\text{m}$
2. $\sqrt{29}\text{m}$
3. $9\text{m}$
4. $\sqrt{41}\text{m}$

Q. If the speed of a car is given as $v=3t^2+2t+3\text{m/s}$, total distance covered by the car in $10sec$ is

1. $1230\text{m}$
2. $1030\text{m}$
3. $930\text{m}$
4. $1130\text{m}$

Q. At $t=0$, a particle starts from $(1,0)$ and moves towards positive $x-$axis with speed of $v=3t^2+2t\text{m/s}$. The final position of the particle as a function of time is

1. $\frac{3t^3}{2}-2t^2+1\text{m}$
2. $\frac{3t^3}{2}+2t^2+1\text{m}$
3. $t^3+t^2+1\text{m}$
4. $t^3-t^2+1\text{m}$

Q. A farmer moves along the boundary of a square field of side $10\text{m}$ in $30\text{s}$. What will be the magnitude of displacement of the farmer at the end of $1\text{min}45\text{sec}$?

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

Q. At $t=0$, a particle starts from $(-1,0)$ and moves towards positive $x-$axis with speed of $v=3t^2+2t\text{m/s}$. The final position of the particle and the distance travelled by the particle respectively, as a function of time are

1. $t^3-t^2-1\text{m},t^3-t^2\text{m}$
2. $t^3-t^2+1\text{m},t^3-t^2\text{m}$
3. $t^3+t^2-1\text{m},t^3+t^2\text{m}$
4. $t^3-t^2+1\text{m},t^3+t^2\text{m}$