1. Motion in a straight line is most closely described by which idea?
ⓐ. Position changes with time along any path
ⓑ. Position changes with time on a straight line
ⓒ. Velocity changes with time without a path
ⓓ. Distance from origin is recorded at one instant
Correct Answer: Position changes with time on a straight line
Explanation: Motion means that the position of a body changes with time. For motion in a straight line, the position is restricted to one chosen line, so a single coordinate is enough to describe where the body is located. Examples include a lift moving vertically, a train moving along a straight track, or a runner moving along a straight lane. A single distance reading, a velocity change, or an unspecified path does not by itself give the one-dimensional idea of motion unless position changes with time along the chosen straight line. The phrase “with time” is essential because motion compares positions at different instants.
2. A lift moves from the ground floor to the third floor and then stops. Why is this a suitable example of one-dimensional motion?
ⓐ. Position along one vertical line
ⓑ. Constant mass during the trip
ⓒ. Constant speed at all times
ⓓ. Zero displacement after stopping
Correct Answer: Position along one vertical line
Explanation: One-dimensional motion means motion that can be described along a single straight line. A lift moves up or down along the same vertical line, so its position can be represented by one coordinate on that line. The motion may be fast, slow, uniform, or non-uniform; constant speed is not required for one-dimensional motion. Stopping only means the position is not changing at that instant, not that the whole displacement must be zero. The important feature is the line of motion, not whether the object is moving at a constant rate.
3. To record the position of a train on a straight track, a fixed station \(O\) is chosen as \(x=0\). What role does \(O\) play in this description?
ⓐ. The point where speed is measured
ⓑ. The point where acceleration is zero
ⓒ. The origin for measuring position
ⓓ. The reference for total path length
Correct Answer: The origin for measuring position
Explanation: A position coordinate needs a starting point from which positions are measured. The fixed station \(O\) acts as the origin, so the coordinate \(x\) of the train is measured relative to that point. Without an origin, a statement such as \(x=200\,\text{m}\) would not tell us where the train is located. The origin is not a speed, acceleration, or distance travelled; it is part of the coordinate description. Choosing a different origin changes the numerical coordinate, but it does not move the train physically.
4. On a straight road, east is chosen as the positive direction. A bicycle is moving west. How should the direction of its motion be represented in this coordinate description?
ⓐ. By positive velocity along the chosen axis
ⓑ. By negative velocity along the chosen axis
ⓒ. By zero velocity on the chosen axis
ⓓ. By speed only, with no direction sign
Correct Answer: By negative velocity along the chosen axis
Explanation: In one-dimensional motion, a positive direction is chosen first. If east is positive, then motion toward west is in the negative direction. The negative sign does not mean that the bicycle has no motion or that its speed is negative. It only gives direction relative to the chosen axis. The unit \( \text{m s}^{-1} \) still describes velocity, while the sign tells whether the motion is along or opposite to the positive direction.
5. Match the basic kinematic symbols with their usual meanings.
| Symbol | Meaning |
|---|
| P. \(x\) | 1. Time |
| Q. \(t\) | 2. Acceleration |
| R. \(v\) | 3. Position coordinate |
| S. \(a\) | 4. Velocity |
ⓐ. P-3, Q-1, R-4, S-2
ⓑ. P-1, Q-3, R-4, S-2
ⓒ. P-3, Q-4, R-1, S-2
ⓓ. P-2, Q-1, R-4, S-3
Correct Answer: P-3, Q-1, R-4, S-2
Explanation: The symbol \(x\) commonly denotes the position coordinate of a body on the chosen line. The symbol \(t\) denotes time, while \(v\) denotes velocity and \(a\) denotes acceleration. These symbols help write compact relations later, such as velocity being related to change of position with time. Confusing \(x\) with distance or \(a\) with speed can lead to wrong formula use in later parts of the chapter. The symbols are meaningful only after the coordinate axis and time measurement have been fixed.
6. The SI unit of acceleration is ______.
ⓐ. \( \text{m} \)
ⓑ. \( \text{s} \)
ⓒ. \( \text{m s}^{-1} \)
ⓓ. \( \text{m s}^{-2} \)
Correct Answer: \( \text{m s}^{-2} \)
Explanation: Acceleration describes how velocity changes per unit time. Since velocity has SI unit \( \text{m s}^{-1} \), dividing it by time in \( \text{s} \) gives \( \text{m s}^{-2} \). The unit \( \text{m} \) belongs to position, distance, or displacement, not acceleration. The unit \( \text{m s}^{-1} \) belongs to speed or velocity. The exponent \(-2\) on \( \text{s} \) shows that time appears twice in the denominator when acceleration is expressed in SI units.
7. A runner stays in one straight lane while moving from one end of the track to the other. What makes the motion suitable for description by a single coordinate \(x\)?
ⓐ. Position changes along one chosen line
ⓑ. Speed remains constant in the same lane
ⓒ. The runner returns to the starting point
ⓓ. Displacement is zero in each interval
Correct Answer: Position changes along one chosen line
Explanation: A single coordinate \(x\) is enough when the motion is along one straight line. The runner’s changing position can then be marked by different values of \(x\) on that line. The runner’s mass, shoes, or style of running are not the reason for using one-dimensional kinematics. Returning to the starting point is also not required; a runner may move only forward and still have one-dimensional motion. The coordinate idea depends on the geometry of the path used for description.
8. A box is lying on the floor of a bus moving uniformly along a straight road. For a passenger sitting inside the bus, how is the box best described?
ⓐ. At rest relative to the passenger
ⓑ. Moving backward relative to the passenger
ⓒ. Accelerating upward relative to the passenger
ⓓ. Moving forward relative to the bus floor
Correct Answer: At rest relative to the passenger
Explanation: Rest and motion depend on the frame of reference. The box and the passenger are moving together with the bus, so the position of the box relative to the passenger does not change. For a person standing on the road, the same box is moving along with the bus. This does not create a contradiction because the two observers are using different frames. A body can be at rest in one frame and in motion in another frame at the same time.
9. A lamp post is fixed beside a road. A car passes it and moves away. In the frame of the road, what changes with time for the car?
ⓐ. Its speed unit relative to the road
ⓑ. The time reading of one second
ⓒ. Its position relative to the lamp post
ⓓ. The origin chosen by the road observer
Correct Answer: Its position relative to the lamp post
Explanation: In the road frame, the lamp post can be treated as a fixed reference object. As the car moves away, its position relative to the lamp post changes with time. That change of position is the basic kinematic description of motion. The unit of mass and the value of time do not change because the car moves. The origin is chosen by the observer; it does not shift automatically just because the car passes a point.
10. A straight corridor is marked with an origin \(O\), and the positive direction is to the right. A point \(P\) is \(3\,\text{m}\) to the left of \(O\). What coordinate should be assigned to \(P\)?
ⓐ. \(+3\,\text{m}\)
ⓑ. \(-3\,\text{m}\)
ⓒ. \(0\,\text{m}\)
ⓓ. \(6\,\text{m}\)
Correct Answer: \(-3\,\text{m}\)
Explanation: The coordinate sign is decided by the chosen positive direction. Since the positive direction is to the right, points to the left of the origin have negative coordinates. The point is \(3\,\text{m}\) from \(O\), so its coordinate is \(-3\,\text{m}\). The sign is part of the coordinate description, while the number \(3\,\text{m}\) tells how far the point is from the origin. A negative coordinate does not mean a negative physical length; it means the point lies on the negative side of the axis.
11. Assertion: Rest and motion are relative terms.
Reason: The description of rest or motion can depend on the observer’s frame of reference.
ⓐ. Both Assertion and Reason are true, and Reason explains Assertion
ⓑ. Both Assertion and Reason are true, but Reason does not explain Assertion
ⓒ. Assertion is true, but Reason is false
ⓓ. Assertion is false, but Reason is true
Correct Answer: Both Assertion and Reason are true, and Reason explains Assertion
Explanation: A body is said to be at rest if its position does not change with time in a chosen frame of reference. The same body is said to be in motion if its position changes with time in another frame. For example, a seated passenger is at rest relative to the bus but moving relative to the road. This shows that rest and motion are not absolute descriptions in ordinary kinematics. The Reason gives the exact basis for the Assertion because the observer’s frame decides the position measurement.
12. Changing the origin from one end of a straight track to the middle of the track will most directly change which description of a runner?
ⓐ. The runner’s physical location on the track
ⓑ. The runner’s position coordinate \(x\)
ⓒ. The runner’s total path length
ⓓ. The runner’s time interval of motion
Correct Answer: The runner’s position coordinate \(x\)
Explanation: The physical location of the runner does not change merely because a new origin is chosen. However, the numerical coordinate \(x\) depends on where \(x=0\) is placed. If the origin is shifted, the same point on the track may receive a different coordinate value. This is why position coordinates are always stated relative to an origin and an axis direction. The choice of origin changes the description, not the actual place occupied by the runner.
13. A motion record uses \( \text{m} \), \( \text{s} \), \( \text{m s}^{-1} \), and \( \text{m s}^{-2} \). Which pairing is most suitable for basic one-dimensional kinematics?
ⓐ. \(x\) in \( \text{m} \), \(t\) in \( \text{s} \), \(v\) in \( \text{m s}^{-1} \), \(a\) in \( \text{m s}^{-2} \)
ⓑ. \(x\) in \( \text{s} \), \(t\) in \( \text{m} \), \(v\) in \( \text{m s}^{-2} \), \(a\) in \( \text{m s}^{-1} \)
ⓒ. \(x\) in \( \text{m s}^{-1} \), \(t\) in \( \text{m s}^{-2} \), \(v\) in \( \text{s} \), \(a\) in \( \text{m} \)
ⓓ. \(x\) in \( \text{m s}^{-2} \), \(t\) in \( \text{m s}^{-1} \), \(v\) in \( \text{m} \), \(a\) in \( \text{s} \)
Correct Answer: \(x\) in \( \text{m} \), \(t\) in \( \text{s} \), \(v\) in \( \text{m s}^{-1} \), \(a\) in \( \text{m s}^{-2} \)
Explanation: Position coordinate \(x\) is a length-type quantity, so its SI unit is \( \text{m} \). Time \(t\) is measured in \( \text{s} \). Velocity \(v\) is change of position per unit time, so its unit is \( \text{m s}^{-1} \). Acceleration \(a\) is change of velocity per unit time, so its unit is \( \text{m s}^{-2} \). Unit pairing is not just memory work; it also helps detect whether a later formula has the right physical meaning.
14. In a straight-line description, two observers choose opposite positive directions along the same road. A cyclist is moving toward the east. What can happen to the sign of the cyclist’s velocity in their descriptions?
ⓐ. Positive in both coordinate descriptions
ⓑ. Negative in both coordinate descriptions
ⓒ. Opposite signs in the two descriptions
ⓓ. Zero in one description and non-zero in the other
Correct Answer: Opposite signs in the two descriptions
Explanation: The sign of velocity depends on the chosen positive direction. If one observer chooses east as positive, the eastward velocity is positive in that coordinate system. If another observer chooses west as positive, the same eastward velocity is negative in that coordinate system. The cyclist’s actual motion does not stop or change because the sign convention changes. A sign convention is a language for describing direction, not a force acting on the moving body.
15. Use the arrangement described below. A straight line has origin \(O\). Point \(L\) is \(5\,\text{m}\) to the left of \(O\), and point \(R\) is \(5\,\text{m}\) to the right of \(O\). The positive direction is chosen toward the right. What is the best coordinate description of the two points?
ⓐ. \(L=+5\,\text{m}\), \(R=-5\,\text{m}\)
ⓑ. \(L=-5\,\text{m}\), \(R=+5\,\text{m}\)
ⓒ. \(L=0\,\text{m}\), \(R=+10\,\text{m}\)
ⓓ. \(L=-10\,\text{m}\), \(R=0\,\text{m}\)
Correct Answer: \(L=-5\,\text{m}\), \(R=+5\,\text{m}\)
Explanation: The origin \(O\) is the zero point for position coordinates. Since the positive direction is toward the right, the point on the right has a positive coordinate and the point on the left has a negative coordinate. Both points are equally far from the origin, so the magnitudes of their coordinates are the same. The signs differ because the points lie on opposite sides of \(O\). The coordinate sign tells side of the origin, while the magnitude tells separation from the origin.
16. A person walking inside a train says, “I am moving forward.” A person standing on the platform also sees the train moving forward. Why is a frame of reference still needed to describe the person’s motion clearly?
ⓐ. Because positions are measured in a chosen frame
ⓑ. Because the train frame must use a different unit
ⓒ. Because acceleration must be zero in every frame
ⓓ. Because the platform observer cannot measure position
Correct Answer: Because positions are measured in a chosen frame
Explanation: A frame of reference tells us from where position is being measured. The person’s motion relative to the train may differ from the person’s motion relative to the platform. If the person walks forward inside a train that is also moving forward, the platform frame and train frame may assign different speeds and positions. The need for a frame does not mean the train frame needs a different unit or that motion must have zero acceleration. The unit \( \text{m} \) remains the same, but the coordinate description depends on the chosen reference frame.
17. A phone kept on a seat in a moving train is observed by two people: one sitting beside it in the train and one standing on the platform. The most complete description is that the phone is
ⓐ. at rest in every frame because it does not slide
ⓑ. moving in every frame because the train is moving
ⓒ. at rest in train frame and moving in platform frame
ⓓ. neither at rest nor in motion because observers disagree
Correct Answer: at rest in train frame and moving in platform frame
Explanation: Rest and motion are decided by checking whether position changes with time in a chosen frame of reference. For the passenger sitting beside the phone, the phone’s position relative to the seat remains unchanged, so it is at rest in the train frame. For the person on the platform, the phone moves along with the train, so its position changes with time in the platform frame. The two descriptions are not contradictory because they belong to different reference frames. A clear kinematic statement should mention or imply the frame in which the position is being measured.
18. A straight road is described using a coordinate axis. The town gate is first chosen as origin \(O\), but later a milestone \(2\,\text{km}\) east of the gate is chosen as the new origin. What remains unchanged by this new choice?
ⓐ. The physical location of a parked car on the road
ⓑ. The coordinate \(x\) of every point on the road
ⓒ. The sign of every coordinate on the road
ⓓ. The numerical value of the car’s position coordinate
Correct Answer: The physical location of a parked car on the road
Explanation: Changing the origin changes the coordinate description, not the actual location of objects. A parked car remains at the same physical point on the road whether the origin is the town gate or the milestone. Its coordinate \(x\) may change because position is measured from a different zero point. The sign of the coordinate may also change if the new origin lies on the other side of the car. Coordinates are part of a chosen description, while the physical location is not altered by relabelling the axis.
19. In a one-dimensional record, a cart has coordinate \(x=-6\,\text{m}\) at one instant. This statement by itself tells us that the cart is
ⓐ. moving \(6\,\text{m}\) toward the negative side
ⓑ. located at the origin after moving \(6\,\text{m}\)
ⓒ. located \(6\,\text{m}\) on the negative side
ⓓ. accelerating toward the negative side of the axis
Correct Answer: located \(6\,\text{m}\) on the negative side
Explanation: A negative position coordinate tells where the body is relative to the chosen origin and positive direction. The coordinate \(x=-6\,\text{m}\) means the cart is \(6\,\text{m}\) from the origin on the negative side of the axis. It does not tell whether the cart is moving, at rest, speeding up, or slowing down. Direction of motion needs information about how position changes with time, not just one position value. A coordinate sign should not be confused with the sign of velocity.
20. Study the position records of a toy car on a straight line.
| Time | Position coordinate |
|---|
| \(t=0\,\text{s}\) | \(x=+2\,\text{m}\) |
| \(t=1\,\text{s}\) | \(x=+2\,\text{m}\) |
| \(t=2\,\text{s}\) | \(x=+2\,\text{m}\) |
What does the table show in the chosen frame?
ⓐ. The car is at rest at \(x=+2\,\text{m}\)
ⓑ. The car is moving in the positive direction
ⓒ. The car is moving in the negative direction
ⓓ. The car has zero velocity at \(x=+2\,\text{m}\)
Correct Answer: The car is at rest at \(x=+2\,\text{m}\)
Explanation: In a given frame, a body is at rest when its position coordinate does not change with time. Here the coordinate remains \(x=+2\,\text{m}\) at \(t=0\,\text{s}\), \(t=1\,\text{s}\), and \(t=2\,\text{s}\). The positive coordinate only tells that the car is on the positive side of the origin. It does not mean the car is moving in the positive direction. A constant position coordinate represents rest in that chosen frame.
