Displacement

Q.

A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps forward and 3 steps backward, and so on. Each step is 1 m long and requires 1 s. Plot the x-t graph of his motion. Determine graphically and otherwise how long the drunkard takes to fall in a pit 13 m away from the start.

Q. A man goes $10\text{m}$ towards North, then $20\text{m}$ towards east. Then, total length of displacement is

1. $25\text{m}$
2. $25.5\text{m}$
3. $30\text{m}$
4. $22.4\text{m}$

Q.

A drunkard is walking along a straight road. He takes 5 steps forward and 3 steps backward and so on. Each step is 1 m long and takes 1 s. There is a pit on the road 11 m away from the starting point. The drunkard will fall into the pit after:

1. 37 s
2. 21 s
3. 29 s
4. 31 s

Q.

The position of a body moving along x-axis at t is given by x=(t²-4t+6)m. The distance travelled by body in time interval t=0 to t=3 s is
(A) 5m
(B) 7m
(C) 4m
(D) 3m

Q. An object moves from point A to point B to point C, then back to point B and then to point C along the line shown in the figure. Find the magnitude of displacement covered by the moving object in $\text{km}$.

1. 13
2. 11
3. 9
4. 7

Q. An object moves along the grid through the points A, B, C, D, E and F as shown in the figure. Find the magnitude of displacement covered by the moving object.

1. $1.5\text{km}$
2. $2\text{km}$
3. $2.5\text{km}$
4. $3\text{km}$

Q. The displacement of the point of the wheel initially in contact with the ground, when the wheel rolls forward half a revolution will be (radius of the wheel is $R$)

1. $2\pi R$
2. $\pi R$
3. $\frac{R}{\sqrt{{\pi }^2+1}}$
4. $R\sqrt{{\pi }^2+4}$

Q. A car travels $6\text{km}$ towards the north at an angle ${45}^{\circ }$ to the East and then travels distance of $4\text{km}$ towards the north at an angle ${135}^{\circ }$ to the east. How far is the point from the starting point ? What angle does the straight line joining its initial and final positions, makes with the east ?

1. $\sqrt{50}\text{km}$ and $ta{n}^{-1}\left(5\right)$
2. $\sqrt{10}\text{km}$ and $ta{n}^{-1}\left(\sqrt{5}\right)$
3. $\sqrt{52}\text{km}$ and $ta{n}^{-1}\left(5\right)$
4. $\sqrt{52}\text{km}$ and $ta{n}^{-1}\left(\sqrt{5}\right)$

Q. A hall has the dimensions $10m\times 10m\times 10m.$ A fly starting at one corner ends up at a diagonally opposite corner. The magnitude of its displacement is nearly

1. $5\sqrt{3}m$
2. $10\sqrt{3}m$
3. $20\sqrt{3}m$
4. $30\sqrt{3}m$

Q. A Body moves 6 m north. 8 m east and 10m vertically upwards, what is the magnitude of its resultant displacement from initial position?

1. 
2. 
3. 
4. 

Q. A monkey staBeing on the ground wants to climb to the top of a vertical pole of 15m.he climbs 5m in 1s and slips downward 3m in next second. He keeps climbing up in this manner. Find the time taken by the monkey to climb to the top of the pole.

Q. A particle starts from the origin, goes along x-axis to the point (20m, 0) and then returns along the same line to the point (20m, 0). The distance and the displacement of the particle during the trip are
a. 40m, 0
b. 40m, 20m
c. 40m, -20m
d. 60m, -20m

Q. A drunkard takes a step of $1\text{m}$ in 1 second. He takes 5 steps forward and 3 steps backwards, and so on. The time taken by him to fall in a pit $13\text{m}$ away from the starts is

1. 26 seconds
2. 31 seconds
3. 37 seconds
4. 41 seconds

Q. Derive position time relation by graphical method

Q. Velocity-time equation of a particle moving in a straight line is, $v=(10+2t+3t^2)$. Find displacement of particle from the origin at time $t=1\text{s}$, if it is given that displacement is $20\text{m}$ at time $t=0$

1. $16\text{m}$
2. $64\text{m}$
3. $48\text{m}$
4. $32\text{m}$

Q.

A body is released from the top of a tower of height H m. After 2 s, it is stopped and then instaneously released. What will be its height after next 2 s ?

1. (H-5) m

2. (H-10) m

3. (H-20) m

4. (H-40) m

Q.

A body starts from rest with uniform acceleration. The velocity of the body after t seconds is v. The displacement of the body in last three seconds is

1. $\frac{3v}{2\left(t-3\right)}$

2. $\frac{3v}{2\left(t+3\right)}$

3. $3v\left(1-\frac{3}{2t}\right)$

4. $3v\left(1+\frac{3}{2t}\right)$

Q.

The displacement x of a particle at the instant when its velocity is v is given by $v=\sqrt{3x+16}$. Its acceleration and initial velocity are

1. 1.5 unit, 4 unit

2. 3 unit, 4 unit

3. 16 unit, 1.6 unit

4. 16 unit, 3 unit

Q.

A boy starts from his house and travels $5\mathrm{km}$ to reach his school. On finding it closed, he returns to his house. What is,

(a) the distance travelled by the boy (b) the final displacement of the boy.

Q.

A particle moves along a circular path from one point to a diametrically opposite point, what is the magnitude of its displacement?

Q. A football is kicked 20m/s at a projection angle of 45°. A receiver on the goal line 25 m away in the direction of the kick runs the same instant to meet the ball. What must be his speed, if he is to catch the ball before it hits the ground??

Q. A man weighing 80 kg is standing at the centre of a flat boat and he is 20 m away from the shore. He walks 8 m on the boat towards the shore and then comes to a halt. The boat weighs 200 kg. How far is he from the shore at the end of this time?

1. 11.2 m
2. 13.8 m
3. 14.3 m
4. 15.4 m

Q. If velocity depends on time such that $v=4-2t$. Find out distance travelled by particle from $1$ to $3\text{s}$.

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

Q. A man goes $12\text{m}$ towards North, then $5\text{m}$ towards east. Then, total length of displacement is

1. $13\text{m}$
2. $15\text{m}$
3. $12\text{m}$
4. $5\text{m}$

Q. Choose the correct option:
i. Distance can be negative.
ii. Displacement can't be greater than Distance.
iii. Displacement is always less than Distance.
iv. Displacement can be equal to Distance.

1. ii & iii
2. ii & iv
3. i & iii
4. ii, iii & iv

Q. A man goes $10\text{m}$ towards North, then $20\text{m}$ towards east. Then, total length of displacement is

1. $22.4\text{m}$
2. $25\text{m}$
3. $25.5\text{m}$
4. $30\text{m}$

Q. A person moves $30m$ north and then $20m$ towards east and finally $30\sqrt{2}m$ in south-west direction. The displacement of the person from the origin will be

1. $10m$along north
2. $10m$ long south
3. $10m$along west
4. $Zero$

Q. A person moves $30m$ north and then $20m$ towards east and finally $30\sqrt{2}m$ in south-west direction. The displacement of the person from the origin will be

1. 10 m along north
2. 10 m long south
3. 10 m along west
4. Zero

Q.

For the motion on a straight-line path with a constant acceleration, the ratio of the magnitude of the displacement to the distance covered is

1. $=1$

2. $\ge 1$

3. $\le 1$

4. $<1$

Q.

What is difference between path length and distance?(not displacement)