Describing Motion Questions in English

(N/A) Yes,an object can have zero displacement even when it has moved through a distance.
This occurs when the final position of the object coincides with its initial position.
For example,if a person walks around a circular park and returns to the exact starting point,the total distance covered is equal to the circumference of the park,but the displacement is $0$ because the initial and final positions are the same.

(B) Given, side of the square field $= 10 \, m$.
Perimeter of the square field $= 4 \times 10 \, m = 40 \, m$.
The farmer completes one round of the field in $40 \, s$.
Total time taken $= 2 \, min \; 20 \, s = (2 \times 60) \, s + 20 \, s = 140 \, s$.
Number of rounds completed by the farmer $= \frac{\text{Total time}}{\text{Time for one round}} = \frac{140 \, s}{40 \, s} = 3.5 \, \text{rounds}$.
After $3$ complete rounds, the farmer will be back at the starting position. In the remaining $0.5$ round, the farmer will cover half the perimeter, i.e., $20 \, m$, and will reach the diagonally opposite corner of the square.
Let the starting point be $A$ and the diagonally opposite point be $C$. The displacement is the length of the diagonal $AC$.
Using the Pythagorean theorem, $AC = \sqrt{(10 \, m)^2 + (10 \, m)^2} = \sqrt{100 + 100} \, m = \sqrt{200} \, m = 10\sqrt{2} \, m$.
Taking $\sqrt{2} \approx 1.414$, the displacement $= 10 \times 1.414 \, m = 14.14 \, m$.

(D) Displacement is the shortest distance between the initial and final positions of an object.
$1$. Displacement can be zero if the initial and final positions of the object are the same (e.g., in circular motion).
$2$. The magnitude of displacement is always less than or equal to the distance travelled by the object $(|\text{Displacement}| \le \text{Distance})$.
Therefore, both statements $(a)$ and $(b)$ are false. The correct option is $(d)$.

(B) The magnitude of average velocity is defined as the ratio of the total displacement to the total time taken. The average speed is defined as the ratio of the total distance traveled to the total time taken.
For an object moving in a straight line without changing its direction,the total distance traveled is equal to the magnitude of the total displacement.
Therefore,under the condition of motion in a straight line without changing direction,the magnitude of average velocity is equal to the average speed.

(B) The odometer is a device used in automobiles to measure the total distance traveled by the vehicle.
It records the cumulative distance covered from the time the vehicle was manufactured or since the last reset.

(B) Uniform motion is defined as the motion of an object in which it travels equal distances in equal intervals of time along a straight line.
Therefore,the path of an object in uniform motion is always a straight line.

If the distance-time graph is a straight line parallel to the time axis,it indicates that the distance of the object from the reference point remains constant as time passes.
This means the object is not changing its position with respect to time.
Therefore,the object is at rest.

(B) The distance covered from $A$ to $B$ is $300 \, m$.
The time taken to travel from $A$ to $B$ is $2 \, min \, 30 \, sec = (2 \times 60) + 30 = 150 \, s$.
Average speed from $A$ to $B$ is defined as the total distance divided by the total time taken:
$\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{300 \, m}{150 \, s} = 2 \, m s^{-1}$.
Velocity from $A$ to $B$ is defined as the displacement divided by the total time taken. Since the motion is in a straight line from $A$ to $B$,the displacement is equal to the distance $(300 \, m)$:
$\text{Velocity} = \frac{\text{Displacement}}{\text{Total Time}} = \frac{300 \, m}{150 \, s} = 2 \, m s^{-1}$.
Thus,the average speed and velocity from $A$ to $B$ are both $2 \, m s^{-1}$.

(C) Total distance covered from $A$ to $C = AB + BC = 300 \, m + 100 \, m = 400 \, m$.
Total time taken from $A$ to $C = \text{Time for } AB + \text{Time for } BC = (2 \times 60 + 30) \, s + 60 \, s = 150 \, s + 60 \, s = 210 \, s$.
Average speed = $\text{Total distance} / \text{Total time} = 400 \, m / 210 \, s \approx 1.904 \, m s^{-1}$.
Displacement from $A$ to $C = AB - BC = 300 \, m - 100 \, m = 200 \, m$.
Average velocity = $\text{Displacement} / \text{Total time} = 200 \, m / 210 \, s \approx 0.952 \, m s^{-1}$.

(C) Displacement is the shortest path between the initial and final positions,while distance is the total path length covered by an object.
Since the shortest path is always less than or equal to the total path length,the magnitude of displacement is always less than or equal to the distance.
Therefore,the ratio of displacement to distance is always $\leq 1$.

(C) Distance is the total path length covered by an object,while displacement is the shortest distance between the initial and final positions.
When an object moves along a straight-line path without changing its direction,the total distance covered is equal to the magnitude of the displacement.
In cases of circular motion,to-and-fro motion,or orbital motion,the object changes its direction,causing the displacement to be less than the total distance covered.
Therefore,the correct option is $C$.

(B) No,the distance travelled by the object would not necessarily be zero.
Displacement is a vector quantity defined as the shortest distance between the initial and final positions,whereas distance is a scalar quantity representing the total path length covered by the object.
Displacement becomes zero when an object returns to its starting point (initial position = final position) after completing a journey.
However,the object has still covered a path to return to the start,meaning the total distance travelled is greater than zero.
For example,if an athlete runs one complete lap around a circular track,their displacement is $0$,but the distance travelled is equal to the circumference of the track $(2 \pi r)$.

(B) When a body is in motion,its position changes with respect to time.
Consequently,the distance covered by the body and its displacement from the initial point change continuously.
Therefore,distance or displacement are the physical quantities that essentially change as a body moves.

(B) The magnitude of displacement is the shortest distance between the initial and final positions of an object.
Distance is the total path length covered by the object.
When an object moves along a straight line without changing its direction,the total path length covered is exactly equal to the straight-line distance between the starting and ending points.
Therefore,the magnitude of displacement is equal to the distance travelled only when the object moves along a straight line in one direction.

(B) Distance is the total path length covered by an object,while displacement is the shortest distance between the initial and final positions.
For the magnitude of displacement to be equal to the distance,the object must move in a straight line in a single direction without any change in direction.
If the object changes its direction,the total path length (distance) will be greater than the straight-line distance (displacement) between the start and end points.

(C) Displacement is defined as the shortest distance between the initial position and the final position of an object.
In this scenario,both the boy and the football start from the same initial position (where the boy kicks the ball) and end at the same final position (where the boy catches the ball).
Since the initial and final positions are identical for both,their displacement is equal.
Although the path taken by the football is a curved trajectory (projectile motion) and the path taken by the boy is a straight or curved path on the ground,the displacement depends only on the start and end points,not the path taken.

(B) The distance covered by a body is equal to the magnitude of its displacement when the body moves along a straight-line path in a single direction.
In this scenario,the path length (distance) is identical to the straight-line distance between the initial and final positions (displacement).
If the body reverses its direction,the distance will be greater than the magnitude of the displacement.

(B) No,it is not possible. Distance is the total path length covered by an object. If an object moves,it must cover some distance. Displacement is the shortest distance between the initial and final positions. If displacement is not zero,it means the object has changed its position,which implies that the object must have moved,and therefore,the distance travelled cannot be zero.

(A) The displacement $s$ of a body is proportional to the time $t$ elapsed,which can be expressed as $s \propto t$ or $s = kt$,where $k$ is a constant representing velocity.
Since the velocity $(v = ds/dt = k)$ remains constant over time,the body is said to be in uniform motion.
Therefore,the correct answer is uniform motion.

(C) An object in motion is considered to be a point object if the distance it travels is very large compared to the dimensions (size) of the object itself. In such cases,the size of the object becomes negligible relative to the path covered.

(A) Yes,the displacement of a particle can be zero even when the distance travelled is not zero.
This occurs when an object moves along a closed path and returns to its initial position.
For example,if a particle moves in a circular path of radius $r$ and completes one full revolution,the distance travelled is the circumference of the circle $(2\pi r)$,while the displacement is $0$ because the final position coincides with the initial position.

(N/A)

Distance	Displacement
$(i)$ It is the actual path length travelled by the body.	$(i)$ It is the shortest distance between the initial and final positions.
$(ii)$ It is a scalar quantity.	$(ii)$ It is a vector quantity.
$(iii)$ It cannot be zero for a moving body.	$(iii)$ It can be zero,positive,or negative.

(N/A) Distance is the length of the actual path traversed between the initial and final positions of an object. It is a scalar quantity and can never be negative.
Displacement is the shortest path between the initial and final positions of an object. It is a vector quantity and can be positive,negative,or zero.

(N/A) Rest and motion are relative terms because they depend on the frame of reference of the observer.
For example,consider a passenger sitting inside a moving train.
With respect to another passenger sitting in the same compartment,the passenger is in a state of rest because their relative position does not change with time.
However,with respect to an observer standing on the platform outside the train,the same passenger is in a state of motion because their position changes continuously as the train moves.
Thus,the state of rest or motion is not absolute but depends on the observer's frame of reference.

(N/A) The reference point chosen is the Post Office,which acts as the origin of the motion.
Since the friend travels in a straight line from the Post Office to Ravi's house,the path length is equal to the shortest distance between the two points.
Distance is the total path length covered,which is $1 \,km$.
Displacement is the shortest distance between the initial position (Post Office) and the final position (Ravi's house),which is $1 \,km$ in the southward direction.
Therefore,both the distance and the magnitude of displacement are $1 \,km$.

(N/A) body is said to be in uniform motion if it travels equal distances in equal intervals of time,no matter how small these time intervals may be.
For example,a car moving at a constant speed of $10 \ m/s$ will cover equal distances of $10 \ m$ every second,so its motion is uniform.
The distance-time graph for uniform motion is a straight line as shown in the figure.

(B) Uniform motion is defined as the motion of an object in which it travels equal distances in equal intervals of time,implying that the velocity of the object remains constant over time.
Since the initial velocity is $10 \, m s^{-1}$ and the motion is uniform,there is no acceleration $(a = 0)$.
Therefore,the velocity of the body will remain unchanged at $10 \, m s^{-1}$ even after $10 \, s$.

(D) Displacement is a vector quantity defined as the shortest distance between the initial and final positions of an object in a specific direction.
Since both cars cover the same distance $d$ in one hour in opposite directions (north and south),their displacement will be $d$ towards the north for the first car and $d$ towards the south for the second car.

(N/A) Graphically,the path forms a right-angled triangle where the base is $4\, km$ and the perpendicular height is $3\, km$.
The resultant displacement is the hypotenuse of this triangle.
Using the Pythagorean theorem:
$S = \sqrt{(4\, km)^2 + (3\, km)^2}$
$S = \sqrt{16 + 9}\, km$
$S = \sqrt{25}\, km$
$S = 5\, km$
Thus,the resultant displacement is $5\, km$.

(B) The path followed by an object projected into the air,which is subject only to the acceleration of gravity,is called a $Trajectory$. This path is typically parabolic in shape.

(A) Both have undergone the same displacement. Displacement is defined as the shortest distance between the initial and final positions. Since both the boy and the football started at the same initial position and ended at the same final position,their displacement is identical,even though the football travelled a longer path (distance) through the air.
$(b)$ The values observed in Raman include critical thinking,scientific temperament,and the ability to engage in constructive peer discussion to resolve misconceptions.

(N/A) To calculate the total distance and displacement,we represent the motion on a coordinate system.
$1$. Total Distance:
Distance is the total path length covered by the hiker.
Total Distance $= 700\, m + 300\, m + 400\, m + 600\, m + 1200\, m + 300\, m + 100\, m = 3600\, m$.
$2$. Displacement:
Displacement is the shortest distance between the initial and final positions.
Let the starting point $O$ be $(0, 0)$.
- Move $700\, m$ North: Position $(0, 700)$.
- Move $300\, m$ East: Position $(300, 700)$.
- Move $400\, m$ North: Position $(300, 1100)$.
- Move $600\, m$ West: Position $(300 - 600, 1100) = (-300, 1100)$.
- Move $1200\, m$ South: Position $(-300, 1100 - 1200) = (-300, -100)$.
- Move $300\, m$ East: Position $(-300 + 300, -100) = (0, -100)$.
- Move $100\, m$ North: Position $(0, -100 + 100) = (0, 0)$.
Since the final position $(0, 0)$ is the same as the initial position,the displacement is $0\, m$.

(N/A) $(i)$ Taking house $A$ as the origin $(0 \ m)$,the positions of the houses are: $A = 0 \ m, B = 10 \ m, C = 20 \ m, D = 30 \ m, E = 40 \ m$.
$(ii)$ Position of house $C = 20 \ m$ and position of house $E = 40 \ m$. The position of $C$ relative to $E$ is $20 \ m - 40 \ m = -20 \ m$. This means house $C$ is $20 \ m$ to the left of house $E$.
$(iii)$ Taking house $B$ as the reference point $(0 \ m)$,the position of house $A$ is $-10 \ m$ and the position of house $D$ is $20 \ m$.

(N/A) Distance is the total path length covered by an object,whereas displacement is the shortest distance between the initial and final positions of an object.
Distance is a scalar quantity,while displacement is a vector quantity.
Distance can never be negative or zero for a moving object,whereas displacement can be positive,negative,or zero.
$(b)$ The magnitude of average velocity is equal to the average speed when an object moves along a straight-line path in a single direction without changing its direction of motion.

(N/A) Since the body travels a distance $h$ upwards and $h$ downwards,the total distance travelled is $h + h = 2h$.
$(b)$ As the body returns to its starting point,the displacement is $0$.
The magnitude of the displacement is equal to the distance travelled if the object moves along a straight line in a single direction without changing its direction.

(C) $1$. Distance is the total path length covered by the body. For three-quarters of a circle, the distance is $\frac{3}{4}$ of the circumference $(2\pi r)$.
Distance $= \frac{3}{4} \times 2\pi r = \frac{3\pi r}{2}$.
$2$. Displacement is the shortest straight-line distance between the initial and final positions. If the body starts at point $A$ and moves three-quarters of the circle to point $B$, the angle subtended at the center is $270^{\circ}$ (or $-90^{\circ}$).
$3$. The initial position vector is $(r, 0)$ and the final position vector is $(0, -r)$.
The displacement magnitude is the hypotenuse of a right-angled triangle with sides $r$ and $r$.
Displacement $= \sqrt{r^2 + r^2} = \sqrt{2r^2} = \sqrt{2}r$.

(TRUE) The statement is True.
Kinematics is a branch of mechanics that describes the motion of objects (points,bodies,and systems of bodies) without considering the forces that cause them to move. It focuses on parameters such as position,velocity,acceleration,and time.

(FALSE) The statement is False.
Rectilinear motion is defined as the motion of an object along a straight line.
Motion along a curved path is known as curvilinear motion.
Translatory motion refers to motion where all parts of a body move in the same direction at the same time,which can occur along a straight or curved path,but it is not synonymous with rectilinear motion.

(TRUE) The statement is True.
Definition: An object is said to be at rest if its position does not change with respect to a fixed reference point (or frame of reference) as time passes.

(B) The statement is False.
$A$ quantity that is specified by both magnitude and direction is known as a vector quantity.
$A$ scalar quantity is a physical quantity that is specified only by its magnitude,such as distance,speed,or mass.

(A) The statement is $True$.
Uniform motion is defined as the motion of an object in which the object travels equal distances in equal intervals of time along a straight line. Since displacement is the shortest distance between two points in a specific direction,undergoing equal displacements in equal intervals of time is the fundamental characteristic of uniform motion.