Rectilinear Motion of Particles - Meaning, Example, Types, FAQs

Edited By Vishal kumar | Updated on Jul 02, 2025 04:33 PM IST

What is meant by rectilinear motion? or Define rectilinear motion. or Rectilinear motion definition.

Rectilinear meaning: The body is in motion when the position of an object varies with respect to time and its surroundings. Motion can be defined mathematically using displacement, velocity, and acceleration in a specific frame of reference. A particle's motion can be classed based on its trajectory, with the rectilinear motion of a particle being the most basic. The vectors of displacement, velocity, and acceleration are limited to one dimension.

This Story also Contains

What is meant by rectilinear motion? or Define rectilinear motion. or Rectilinear motion definition.
Example of rectilinear motion of a particle-
Characteristics of rectilinear motions-

Rectilinear Motion of Particles - Meaning, Example, Types, FAQs

Rectilinear motion

Rectilinear (or linear) motion is defined as a particle's movement constrained to a straight line. Only one coordinate can be used to describe such a motion. The particle's displacement, as well as its derivatives, such as velocity and acceleration, are all one-dimensional vectors. A car going along a straight path in free fall under the gravitational field of the Earth can be modeled as a rectilinear motion of a particles

Also read -

Example of rectilinear motion of a particle-

Free fall under gravity and the simple harmonic motion of a mass linked to a spring are examples of the rectilinear motion of a particle.
Elevators are an example of rectilinear motion is of rectilinear mobility in public areas.
Rectilinear motion is caused by gravitational forces acting on objects, culminating in free fall.
The motion of children sliding down a slide is rectilinear.
Planes in the sky move in a rectilinear pattern.

NEET Highest Scoring Chapters & Topics

This ebook serves as a valuable study guide for NEET exams, specifically designed to assist students in light of recent changes and the removal of certain topics from the NEET exam.

Download E-book

Types of rectilinear motion-

There are three different types of rectilinear motion:

Uniform rectilinear motion occurs when an item moves at a constant speed with no acceleration.
Uniformly accelerated rectilinear motion occurs when an object moves with a consistent rate of acceleration.
Rectilinear movement with non-uniform acceleration: A rectilinear movement with non-uniform acceleration occurs when an object moves at an uneven speed and acceleration.

Related Topics,

Characteristics of rectilinear motions-

It follows a straight-line path.
It lacks normal (centripetal) acceleration, which, as you may recall, is what causes the motion to shift direction.

What is linear motion?

Linear motion is one-dimensional motion in a straight line that can be mathematically described with only one spatial dimension.

Linear motion example- Linear motion is demonstrated by a ball tossed straight up and falling straight down.

LINEAR MOTION

Mathematical form of motion-

A one-dimensional reference frame with an axis (X-axis) and an origin at O (x = 0) is used to qualitatively evaluate rectilinear motion.

Position, distance, and displacement:

A particle's position is a vector quantity that is measured from the origin to the particle. The distance between them determines its magnitude. When you set a particle in motion, it follows a route that changes its position over time. Displacement is the vector difference in position after a time interval, pointing from the initial to the final location. The overall path covered along the trajectory is measured in distance, whereas the shortest path is measured in displacement. The displacement is provided by, if the particle's position moves from xi to xf in time t.

x=xf−xi

Speed and velocity-

The temporal rate of change of displacement is termed velocity, while the rate of change of distance is called speed. While speed is a scalar, velocity is a vector with the same direction as displacement. At time t, the instantaneous velocity is given by,

$$
\mathrm{V}=\mathrm{d} x / \mathrm{dt}
$$
Acceleration-
The time rate of change is defined as acceleration when velocity changes over time. It's a vector, too.

$$
\mathrm{A}=\mathrm{dv} / \mathrm{dt}=\mathrm{d}^{\wedge} 2 \mathrm{x} / \mathrm{dt} \mathrm{t}^{\wedge} 2
$$
Because all vectors are confined to one dimension, only the magnitudes need to be considered.

Also, check-

NCERT Physics Notes:

Frequently Asked Questions (FAQs)

1. What are the Rectilinear Motion Categories?

There are three types of rectilinear motion:

The motion of a body with zero acceleration is known as uniform motion. There is no net force operating on the body.
Uniformly accelerated motion is defined as motion with a non-zero constant acceleration and a constant net force on the system.
Non-uniform acceleration motion. The system is subjected to a variable force.

2. What words do you use to characterize linear motion?

Linear motion is an object's natural motion: it moves in a straight path. Newton's First Law of Motion states that an item that is not affected by any force will continue in a straight line eternally.

3. What is the practical application of linear motion?

In everyday life, there are many examples of linear motion, such as when an athlete runs on a straight track. Linear motion is used on a regular basis. A car travelling down a straight road is an illustration of this. Cars, in fact, alternate between linear and circular motion all the time.

4. What are the similarities and differences between rectilinear and circular motion?

Rectilinear motion describes the movement of an object in a straight line. A train on a track, a parade, and coins hurled in the air are all examples of rectilinear motion. The motion of an object that moves at a given distance from a fixed point is known as circular motion. All of the objects in this scene rotate in a circular manner.

5. How does rectilinear motion differ from curvilinear motion?

Rectilinear motion occurs along a straight line, while curvilinear motion follows a curved path. In rectilinear motion, the direction of movement remains constant, whereas in curvilinear motion, the direction changes continuously.

6. Can a particle in rectilinear motion have varying speed?

Yes, a particle in rectilinear motion can have varying speed. The speed can increase (acceleration), decrease (deceleration), or remain constant (uniform motion) while still moving along a straight line.

7. What is uniform rectilinear motion?

Uniform rectilinear motion is when an object moves along a straight line with constant speed. In this type of motion, the velocity remains constant, meaning there is no acceleration or deceleration.

8. What is the difference between distance and displacement in rectilinear motion?

Distance is the total length of the path traveled by an object, while displacement is the shortest straight-line distance between the initial and final positions. In rectilinear motion, distance and displacement may be equal if the object moves in one direction only.

9. How is velocity different from speed in rectilinear motion?

Velocity is a vector quantity that includes both speed and direction, while speed is a scalar quantity that only measures how fast an object is moving. In rectilinear motion, the magnitude of velocity equals the speed, but velocity also indicates the direction of motion.

10. Can an object in rectilinear motion have zero velocity but non-zero acceleration?

Yes, this situation can occur at the moment when an object changes its direction of motion. For example, when a ball is thrown straight up, it has zero velocity at its highest point but still experiences downward acceleration due to gravity.

11. How can you determine if a particle is undergoing rectilinear motion from its position-time graph?

If the position-time graph is a straight line (either sloped or horizontal), the particle is undergoing rectilinear motion. A curved line would indicate non-rectilinear (curvilinear) motion.

12. How is acceleration defined in rectilinear motion?

Acceleration in rectilinear motion is the rate of change of velocity with respect to time. It can be positive (increasing speed), negative (decreasing speed), or zero (constant speed).

13. What is the significance of the slope of a position-time graph in rectilinear motion?

The slope of a position-time graph represents the velocity of the object. A positive slope indicates motion in the positive direction, a negative slope indicates motion in the negative direction, and a horizontal line (zero slope) indicates the object is at rest.

14. How is instantaneous velocity different from average velocity in rectilinear motion?

Instantaneous velocity is the velocity of an object at a specific instant or point in time, while average velocity is the total displacement divided by the total time taken over a given interval. In non-uniform rectilinear motion, these values may differ.

15. What is rectilinear motion?

Rectilinear motion is the movement of an object along a straight line. In this type of motion, the path of the object can be described by a single coordinate, and the direction of motion remains constant.

16. Can an object in rectilinear motion have constant speed but varying velocity?

No, in rectilinear motion, if the speed is constant and the motion is along a straight line, the velocity must also be constant. Velocity can only change if there's a change in speed or direction, but direction remains constant in rectilinear motion.

17. What is meant by 'equations of motion' in rectilinear motion, and why are they important?

Equations of motion in rectilinear motion are mathematical relationships that describe the motion of objects along a straight line. They relate quantities such as displacement, velocity, acceleration, and time. These equations are important because they allow us to predict and analyze the motion of objects under various conditions.

18. What is the difference between kinematics and dynamics in the context of rectilinear motion?

Kinematics in rectilinear motion deals with the description of motion without considering the causes, focusing on quantities like position, velocity, and acceleration. Dynamics, on the other hand, considers the forces that cause the motion and how they affect the object's behavior.

19. How does the concept of frames of reference apply to rectilinear motion?

A frame of reference in rectilinear motion is a coordinate system used to describe the position and motion of objects. The choice of frame can affect how motion is perceived and described. For example, an object may appear to be in rectilinear motion in one frame but stationary in another.

20. What is the difference between average acceleration and instantaneous acceleration in rectilinear motion?

Average acceleration is the change in velocity divided by the time interval over which the change occurs, while instantaneous acceleration is the acceleration at a specific moment in time. In non-uniform acceleration, these values may differ.

21. What is the significance of the area under an acceleration-time graph in rectilinear motion?

The area under an acceleration-time graph represents the change in velocity over the given time interval. This is because velocity is the integral of acceleration with respect to time.

22. What is the difference between elastic and inelastic collisions in rectilinear motion?

In elastic collisions, both momentum and kinetic energy are conserved, while in inelastic collisions, only momentum is conserved. In rectilinear motion, this affects how objects behave after collision, with elastic collisions resulting in objects bouncing apart and inelastic collisions potentially resulting in objects sticking together.

23. How can dimensional analysis be used to verify equations in rectilinear motion?

Dimensional analysis involves checking that the units on both sides of an equation are consistent. In rectilinear motion, this technique can be used to verify that equations are potentially correct and to derive relationships between quantities when the exact form of the equation is unknown.

24. What is the physical meaning of the area under a position-time graph in rectilinear motion?

The area under a position-time graph doesn't have a direct physical meaning in rectilinear motion. However, the slope of this graph at any point represents the instantaneous velocity at that time.

25. What is the significance of the coefficient of restitution in collisions during rectilinear motion?

The coefficient of restitution is a measure of the "bounciness" of a collision. In rectilinear motion, it helps determine the velocities of objects after a collision, with values ranging from 0 (completely inelastic) to 1 (perfectly elastic).

26. What does a horizontal line on a velocity-time graph represent in rectilinear motion?

A horizontal line on a velocity-time graph represents constant velocity or uniform motion. The object is moving at a steady speed in a constant direction.

27. What causes a change in velocity during rectilinear motion?

A change in velocity during rectilinear motion is caused by acceleration or deceleration. This can be due to external forces acting on the object, such as friction, gravity, or applied forces.

28. How is jerk related to rectilinear motion?

Jerk is the rate of change of acceleration with respect to time. In rectilinear motion, jerk describes how quickly the acceleration of an object is changing, which can affect the smoothness of motion.

29. What is the relationship between position, velocity, and acceleration in rectilinear motion?

In rectilinear motion, velocity is the rate of change of position with respect to time, and acceleration is the rate of change of velocity with respect to time. Mathematically, velocity is the first derivative of position, and acceleration is the second derivative of position or the first derivative of velocity.

30. How does air resistance affect rectilinear motion?

Air resistance acts as a force opposing the motion of an object. In rectilinear motion, it can cause deceleration, reducing the object's speed over time. The effect becomes more significant at higher speeds and for objects with larger surface areas.

31. How can the area under a velocity-time graph be interpreted in rectilinear motion?

The area under a velocity-time graph represents the displacement of the object. This is because displacement is the product of velocity and time, which is geometrically represented by the area under the velocity-time curve.

32. What is the significance of the slope of a velocity-time graph in rectilinear motion?

The slope of a velocity-time graph represents the acceleration of the object. A positive slope indicates positive acceleration (speeding up), a negative slope indicates negative acceleration (slowing down), and a horizontal line (zero slope) indicates constant velocity (no acceleration).

33. Can an object in rectilinear motion have zero displacement but non-zero distance traveled?

Yes, this can happen if the object moves back and forth along a straight line, returning to its starting point. The total distance traveled would be the sum of all movements, while the displacement would be zero.

34. How does gravity affect rectilinear motion of a particle thrown vertically upward?

Gravity causes a constant downward acceleration of approximately 9.8 m/s² (on Earth). For a particle thrown vertically upward, this results in a decrease in upward velocity until it reaches zero at the highest point, then an increase in downward velocity as it falls back down.

35. What is the difference between scalar and vector quantities in rectilinear motion?

Scalar quantities, like speed and distance, have only magnitude, while vector quantities, like velocity and displacement, have both magnitude and direction. In rectilinear motion, the direction of vector quantities is constrained to a straight line.

36. How can you determine the direction of acceleration in rectilinear motion?

In rectilinear motion, if the speed is increasing, the acceleration is in the same direction as the velocity. If the speed is decreasing, the acceleration is in the opposite direction to the velocity.

37. What is the role of initial conditions in solving rectilinear motion problems?

Initial conditions, such as initial position and initial velocity, are crucial for solving rectilinear motion problems. They provide the starting point for calculations and help determine the object's subsequent motion based on the given equations of motion.

38. How does the principle of superposition apply to rectilinear motion?

The principle of superposition in rectilinear motion states that when multiple forces act on an object, the resulting motion can be determined by adding the effects of each force individually. This principle allows for the analysis of complex motions by breaking them down into simpler components.

39. How does the concept of relative motion apply to rectilinear motion?

Relative motion in rectilinear motion refers to the motion of one object as observed from another object, which may itself be moving. The relative velocity between two objects in rectilinear motion is the difference between their individual velocities.

40. How does the concept of inertia relate to rectilinear motion?

Inertia is the tendency of an object to resist changes in its state of motion. In rectilinear motion, an object at rest tends to stay at rest, and an object in motion tends to stay in motion in a straight line, unless acted upon by an external force.

41. What is the role of friction in rectilinear motion?

Friction is a force that opposes the relative motion of objects in contact. In rectilinear motion, friction can cause deceleration, eventually bringing moving objects to a stop if no other forces are applied to maintain the motion.

42. How does the mass of an object affect its acceleration in rectilinear motion?

According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In rectilinear motion, this means that for a given force, a more massive object will experience less acceleration than a less massive object.

43. What is the significance of terminal velocity in rectilinear motion?

Terminal velocity is the maximum velocity attainable by an object falling through a fluid (like air) when the resistance of the fluid balances the force of gravity. In rectilinear motion, it represents the point at which acceleration becomes zero, and the object continues to fall at a constant speed.

44. How can energy conservation be applied to rectilinear motion problems?

The principle of energy conservation states that the total energy of an isolated system remains constant. In rectilinear motion, this can be applied to problems involving gravitational potential energy and kinetic energy, helping to solve for velocities and displacements without needing to consider time explicitly.

45. How does air drag affect the equation of motion for an object in rectilinear motion?

Air drag introduces a force that is proportional to the square of the velocity and acts in the opposite direction of motion. This makes the equation of motion non-linear and more complex, often requiring numerical methods to solve accurately.

46. What is the significance of the time of flight in projectile motion, and how does it relate to rectilinear motion?

Time of flight in projectile motion is the total time an object spends in the air. While projectile motion is two-dimensional, the vertical component of the motion is a form of rectilinear motion affected by gravity. The time of flight can be calculated using the equations of rectilinear motion for the vertical component.

47. How does the concept of momentum apply to rectilinear motion?

Momentum in rectilinear motion is the product of an object's mass and its velocity. It is a vector quantity that describes the "quantity of motion" an object possesses. The conservation of momentum principle is particularly useful in analyzing collisions in rectilinear motion.

48. What is the difference between average speed and average velocity in rectilinear motion?

Average speed is the total distance traveled divided by the total time taken, while average velocity is the total displacement divided by the total time taken. In rectilinear motion, these can differ if the object changes direction, as average velocity takes into account the direction of motion while average speed does not.

49. How does the principle of work-energy theorem apply to rectilinear motion?

The work-energy theorem states that the work done on an object equals the change in its kinetic energy. In rectilinear motion, this principle can be used to relate the force applied to an object, the distance it moves, and the change in its kinetic energy.

50. How does the concept of impulse relate to rectilinear motion?

Impulse is the product of force and the time over which it acts. In rectilinear motion, impulse is equal to the change in momentum of an object. This concept is particularly useful in analyzing collisions and sudden changes in motion.

51. What is the role of centripetal acceleration in rectilinear motion?

Centripetal acceleration is not present in rectilinear motion. It only occurs in circular or curvilinear motion where there is a continuous change in the direction of velocity. Rectilinear motion involves movement along a straight line without any curved path.

52. How can graphical methods be used to solve rectilinear motion problems?

Graphical methods in rectilinear motion involve using position-time, velocity-time, or acceleration-time graphs to analyze motion. These graphs can be used to determine displacement (area under v-t graph), velocity (slope of x-t graph or area under a-t graph), and acceleration (slope of v-t graph).

53. What is the significance of the sign of velocity and acceleration in rectilinear motion?

The sign of velocity indicates the direction of motion relative to the chosen coordinate system. A positive velocity means the object is moving in the positive direction, while a negative velocity means it's moving in the negative direction. The sign of acceleration indicates whether the object is speeding up or slowing down relative to its direction of motion.

54. How does the concept of free fall relate to rectilinear motion?

Free fall is a special case of rectilinear motion where an object moves under the influence of gravity alone, neglecting air resistance. In free fall, objects experience a constant acceleration (g ≈ 9.8 m/s² on Earth) directed downward, resulting in a parabolic velocity-time graph and a quadratic position-time graph.