1. Motion in a plane is best described as motion in which the position of a body changes with respect to:
ⓐ. only one fixed line
ⓑ. only the vertical direction
ⓒ. two coordinates in a plane
ⓓ. time alone, without position
Correct Answer: two coordinates in a plane
Explanation: Motion in a plane means that the body’s position cannot be fully described by a single coordinate alone. Two coordinates, usually along the \(x\)-axis and \(y\)-axis, are needed to locate the body at an instant. This is an extension of straight-line motion, where one coordinate may be enough. The path may be curved or slanting, but the description still uses two perpendicular directions. Time is needed to describe how the position changes, but time alone does not locate the body in space.
2. A stone is thrown obliquely upward from the ground. Its motion is usually treated as motion in a plane because:
ⓐ. its mass changes during flight
ⓑ. it has both horizontal and vertical components
ⓒ. its speed is always zero
ⓓ. its acceleration must be along the horizontal direction
Correct Answer: it has both horizontal and vertical components
Explanation: An obliquely thrown stone moves horizontally as well as vertically. A single straight-line coordinate cannot describe both changes at the same time. The horizontal part is naturally described along the \(x\)-axis, and the vertical part along the \(y\)-axis. This makes projectile motion a standard example of motion in a plane. The motion is not classified this way because of mass change or zero speed; it is classified by the need for two position coordinates.
3. A car moves only along a straight east-west road. Compared with an aircraft changing both altitude and horizontal position, the car’s motion:
ⓐ. necessarily needs two coordinates, but the aircraft needs only one
ⓑ. needs one coordinate, while the aircraft needs more than one.
ⓒ. has no displacement because the road is straight
ⓓ. has acceleration but no velocity
Correct Answer: needs one coordinate, while the aircraft needs more than one.
Explanation: Motion along a fixed straight road can be described by one coordinate measured along that road. The car may move east or west, but it remains on the same line. An aircraft changing altitude and horizontal position cannot usually be located by one coordinate alone. It needs at least two coordinates when its motion is studied in a vertical plane. Straight-line motion is therefore a special simpler case, while plane motion needs a two-coordinate description.
4. In the description of motion in a plane, the pair \((x,y)\) gives:
ⓐ. only the speed of the body
ⓑ. position coordinates in chosen axes
ⓒ. only the observation time in the chosen frame
ⓓ. the mass and acceleration values of the body
Correct Answer: position coordinates in chosen axes
Explanation: The ordered pair \((x,y)\) tells where the body is located relative to the chosen coordinate axes. The value \(x\) gives the position along the \(x\)-axis, while \(y\) gives the position along the \(y\)-axis. These two coordinates together locate a point in a plane. They do not directly give speed, mass, or acceleration. A coordinate pair is about position first; changes in position with time lead to velocity and acceleration.
5. The physical quantity \(\vec{r}\) used in plane motion most commonly represents:
ⓐ. position vector
ⓑ. time interval
ⓒ. mass of the moving body
ⓓ. path length only
Correct Answer: position vector
Explanation: The symbol \(\vec{r}\) is commonly used for the position vector of a body. It gives the position of the body with respect to a chosen origin. Since it is a vector, it includes both magnitude and direction from the origin to the point. In a plane, \(\vec{r}\) is usually described through its \(x\)- and \(y\)-coordinates. Path length is different because it depends on the route followed, while \(\vec{r}\) refers to location from the origin.
6. Match the basic plane-motion quantities with their usual SI units.
| Quantity | Unit |
|---|
| P. Displacement | 1. \(\text{s}\) |
| Q. Time | 2. \(\text{m s}^{-2}\) |
| R. Velocity | 3. \(\text{m}\) |
| S. Acceleration | 4. \(\text{m s}^{-1}\) |
The suitable matching is:
ⓐ. P-1, Q-3, R-4, S-2
ⓑ. P-3, Q-4, R-1, S-2
ⓒ. P-3, Q-1, R-4, S-2
ⓓ. P-4, Q-1, R-3, S-2
Correct Answer: P-3, Q-1, R-4, S-2
Explanation: Displacement measures change in position, so its SI unit is \(\text{m}\). Time is measured in \(\text{s}\). Velocity is displacement per unit time, so its unit is \(\text{m s}^{-1}\). Acceleration is change in velocity per unit time, so its unit is \(\text{m s}^{-2}\). The powers of \(\text{s}\) help separate velocity from acceleration: one time factor appears in velocity, while two time factors appear in acceleration.
7. A river boat moves with respect to the water while the river current also carries it downstream. This situation is naturally treated as motion in a plane when:
ⓐ. the boat’s mass is known
ⓑ. the boat is at rest relative to the river bank
ⓒ. only the depth of the river is measured
ⓓ. both along-river and across-river components are involved
Correct Answer: both along-river and across-river components are involved
Explanation: A river-crossing situation may involve motion across the river and motion along the river due to current. These two directions are usually taken as perpendicular components in a plane. The actual motion seen from the bank is a combined effect of both directions. This makes a two-coordinate description useful. The mass of the boat is not what decides whether the motion is in a plane; the need for two directional components does.
8. The quantity \(\Delta\vec{r}\) in plane motion refers to:
ⓐ. the initial position only
ⓑ. change in position vector
ⓒ. the total time of travel
ⓓ. the speed without direction
Correct Answer: change in position vector
Explanation: The symbol \(\Delta\vec{r}\) means change in the position vector. It connects the initial and final positions of the body. Since it is a vector, it has both magnitude and direction. It is different from the total path length travelled, which may be longer for a curved path. The delta symbol \(\Delta\) signals change, and the arrow over \(\vec{r}\) signals vector character.
9. In a rectangular coordinate frame for plane motion, the origin \(O\) is used as:
ⓐ. the point from which coordinates are measured
ⓑ. the point where every moving body must remain
ⓒ. the direction of velocity at every instant
ⓓ. the unit of acceleration
Correct Answer: the point from which coordinates are measured
Explanation: The origin \(O\) is the reference point of the coordinate system. Coordinates such as \((x,y)\) are measured from this point along the chosen axes. A body need not stay at the origin; the origin is only a reference for locating it. Changing the origin can change coordinate values, even when the physical position of the body has not changed. This is why coordinates are always meaningful only after the reference frame has been chosen.
10. A point has coordinates \((-3\,\text{m}, 4\,\text{m})\) in a rectangular frame. This means the point lies:
ⓐ. \(3\,\text{m}\) along positive \(x\) and \(4\,\text{m}\) along positive \(y\)
ⓑ. \(3\,\text{m}\) along negative \(x\) and \(4\,\text{m}\) along positive \(y\)
ⓒ. \(4\,\text{m}\) along negative \(x\) and \(3\,\text{m}\) along positive \(y\)
ⓓ. \(3\,\text{m}\) along positive \(x\) and \(4\,\text{m}\) along negative \(y\)
Correct Answer: \(3\,\text{m}\) along negative \(x\) and \(4\,\text{m}\) along positive \(y\)
Explanation: \( \textbf{Coordinate reading:} \) The first coordinate gives the \(x\)-position and the second coordinate gives the \(y\)-position.
\( \textbf{Given point:} \) \((-3\,\text{m},4\,\text{m})\).
\( \textbf{x-direction meaning:} \) The value \(-3\,\text{m}\) means \(3\,\text{m}\) on the negative side of the \(x\)-axis.
\( \textbf{y-direction meaning:} \) The value \(4\,\text{m}\) means \(4\,\text{m}\) on the positive side of the \(y\)-axis.
\( \textbf{Sign use:} \) The negative sign belongs only to the \(x\)-coordinate here.
\( \textbf{Position interpretation:} \) The point is left of the origin if positive \(x\) is taken to the right, and above the origin if positive \(y\) is upward.
\( \textbf{Final answer:} \) The point lies \(3\,\text{m}\) along negative \(x\) and \(4\,\text{m}\) along positive \(y\).
11. A moving object is recorded at the same instant as \(x=5\,\text{m}\) and \(y=2\,\text{m}\). The phrase “same instant” is important because:
ⓐ. both coordinates describe one position at the same time
ⓑ. the body can have only \(x\)-motion and no \(y\)-motion
ⓒ. time has the same unit as displacement
ⓓ. the coordinates become independent of the chosen origin
Correct Answer: both coordinates describe one position at the same time
Explanation: In plane motion, the coordinates \(x\) and \(y\) together locate the body at a particular instant. If the two coordinates were taken at different times, they might not describe the same position of the moving body. The same time \(t\) is therefore used when describing both directions. This idea becomes especially important when equations of motion are later applied separately along \(x\) and \(y\). Separate coordinate directions do not mean separate clocks for the two parts of the motion.
12. A path is curved on a sheet of graph paper, and the position of a small bead is marked at different times. A two-dimensional description is needed mainly because:
ⓐ. the bead has no velocity on a curved path
ⓑ. both coordinates may change with time
ⓒ. curved paths cannot be measured in metres
ⓓ. acceleration is absent whenever a path is drawn on paper
Correct Answer: both coordinates may change with time
Explanation: A curved path in a plane usually cannot be described by only one coordinate. As the bead moves, its \(x\)-coordinate and \(y\)-coordinate may both change. The coordinate pair \((x,y)\) gives a complete location on the graph paper. The use of metres is still valid because position and displacement are lengths. Curvature does not remove velocity or acceleration; it only makes direction and coordinate description more important.
13. Read the short record below.
At \(t=0\,\text{s}\), a toy car is at \((0\,\text{m},0\,\text{m})\). At \(t=2\,\text{s}\), it is at \((6\,\text{m},0\,\text{m})\). At \(t=4\,\text{s}\), it is at \((6\,\text{m},5\,\text{m})\).
What does the record show about the car’s motion?
ⓐ. The car has moved only along one fixed coordinate direction during the whole record
ⓑ. The car’s position changed first along \(x\) and later along \(y\)
ⓒ. The car’s time coordinate changed but its position did not
ⓓ. The car’s coordinates are meaningless because one value is zero
Correct Answer: The car’s position changed first along \(x\) and later along \(y\)
Explanation: From \(t=0\,\text{s}\) to \(t=2\,\text{s}\), the \(x\)-coordinate changes from \(0\,\text{m}\) to \(6\,\text{m}\), while the \(y\)-coordinate remains \(0\,\text{m}\). From \(t=2\,\text{s}\) to \(t=4\,\text{s}\), the \(x\)-coordinate remains \(6\,\text{m}\), while the \(y\)-coordinate changes from \(0\,\text{m}\) to \(5\,\text{m}\). This record uses coordinate changes to describe motion in a plane. A zero coordinate is still meaningful because it tells that the point lies on an axis for that coordinate. The same object can have different coordinate changes during different parts of its motion.
14. The pair of axes used in elementary plane motion is usually chosen perpendicular to each other because:
ⓐ. perpendicular axes make every path straight
ⓑ. perpendicular axes remove the need for time
ⓒ. perpendicular axes make acceleration equal to zero
ⓓ. they allow independent readings along two axes
Correct Answer: they allow independent readings along two axes
Explanation: Rectangular coordinate axes are chosen perpendicular because they give a clean way to describe position in two independent directions. The \(x\)-coordinate is read along one axis, and the \(y\)-coordinate is read along the other. This does not force the actual path to be straight; the object may still move along a curved path. The choice of axes is a method of description, not a physical force acting on the object. Time is still needed to describe how the coordinates change during motion.
15. In a coordinate description of plane motion, changing the origin can change:
ⓐ. the mass of the body
ⓑ. the SI unit of time
ⓒ. the coordinate values assigned to the same point
ⓓ. the fact that acceleration is measured in \(\text{m s}^{-2}\)
Correct Answer: the coordinate values assigned to the same point
Explanation: Coordinates are measured relative to a chosen origin. If the origin is shifted, the same physical point may receive different coordinate values. This does not mean the point itself has physically moved. The units of displacement, time, velocity, and acceleration are not changed by shifting the origin. Coordinate values are reference-dependent, while the physical event being described remains the same.
16. A body is at \((2\,\text{m},3\,\text{m})\) at one instant and later at \((2\,\text{m},7\,\text{m})\). The coordinate record most directly shows:
ⓐ. no motion, because the \(x\)-coordinate is unchanged
ⓑ. motion only along the \(y\)-direction during this interval
ⓒ. motion only along the \(x\)-direction during this interval
ⓓ. circular motion about the origin
Correct Answer: motion only along the \(y\)-direction during this interval
Explanation: \( \textbf{Initial position:} \) \((2\,\text{m},3\,\text{m})\).
\( \textbf{Final position:} \) \((2\,\text{m},7\,\text{m})\).
\( \textbf{x-coordinate change:} \) \(2\,\text{m}-2\,\text{m}=0\,\text{m}\), so there is no change along \(x\).
\( \textbf{y-coordinate change:} \) \(7\,\text{m}-3\,\text{m}=4\,\text{m}\), so there is a change along \(y\).
\( \textbf{Coordinate interpretation:} \) The position has changed even though one coordinate stayed constant.
\( \textbf{Direction reading:} \) The change is along the positive \(y\)-direction for this interval.
\( \textbf{Final answer:} \) The record shows motion only along the \(y\)-direction during the interval.
17. Speed and velocity are both used to describe motion, but they differ because:
ⓐ. speed has direction only, while velocity has magnitude only
ⓑ. speed is always negative, while velocity is always positive
ⓒ. speed is measured in \(\text{m}\), while velocity is measured in \(\text{s}\)
ⓓ. speed has magnitude only, while velocity has magnitude and direction
Correct Answer: speed has magnitude only, while velocity has magnitude and direction
Explanation: Speed is a scalar quantity because it gives only how fast a body is moving. Velocity is a vector quantity because it gives both how fast the body is moving and in which direction it is moving. Both speed and velocity have the same SI unit, \(\text{m s}^{-1}\), so the difference is not in the unit. A negative sign attached to one component of velocity may indicate direction along a chosen axis, but speed itself is not a vector direction. The useful distinction is that speed can be found from distance per time, while velocity depends on displacement per time.
18. A quantity is classified as a vector only when it has:
ⓐ. magnitude and unit but no direction
ⓑ. sign but no magnitude
ⓒ. magnitude and direction
ⓓ. numerical value only
Correct Answer: magnitude and direction
Explanation: A vector quantity must have both magnitude and direction. Displacement, velocity, acceleration, and force are examples because their directions affect the physical description. A scalar quantity such as mass or time may have a magnitude and a unit, but it does not need a spatial direction. A sign alone is not enough to make a quantity a vector; the sign may only show positive or negative sense along a chosen line. Direction in space is the feature that separates a vector from a scalar.
19. The table below lists some physical quantities.
| Row | Quantity group | Classification claimed |
|---|
| P | Mass, time, distance | Scalars |
| Q | Displacement, velocity, acceleration | Vectors |
| R | Speed, distance, time | Vectors |
| S | Force, displacement, velocity | Vectors |
The row that does not fit the usual scalar-vector classification is:
ⓐ. Row P
ⓑ. Row Q
ⓒ. Row R
ⓓ. Row S
Correct Answer: Row R
Explanation: Mass, time, and distance are scalar quantities because each has magnitude but no required direction. Displacement, velocity, acceleration, and force are vectors because direction is essential in describing them. Speed is a scalar because it only tells the rate of motion, not the direction of motion. Distance is also scalar because it measures the total path length without direction. Row R wrongly classifies speed, distance, and time as vectors, even though all three are scalars.
20. A runner completes one full round of a circular track and returns to the starting point. For the complete round, the distance covered and displacement are best described as:
ⓐ. distance is zero, displacement is zero
ⓑ. distance is non-zero, displacement is zero
ⓒ. distance is zero, displacement is non-zero
ⓓ. distance and displacement are both equal to the radius
Correct Answer: distance is non-zero, displacement is zero
Explanation: Distance is the total length of the path actually travelled. In one complete round of a circular track, the runner has covered the circumference, so the distance is not zero. Displacement depends only on the initial and final positions. Since the runner returns to the starting point, the initial and final positions are the same. The displacement vector is therefore \(\vec{0}\), even though the runner has certainly travelled a non-zero path length.
