Motion In A Straight Line - Definition, Formulas, Examples, FAQs

Motion In A Straight Line - Definition, Formulas, Examples, FAQs

Vishal kumarUpdated on 02 Jul 2025, 04:42 PM IST

In straight motion, an object’s position continuously changes with time and goes in a linear direction relative to a fixed point. The analysis of this type of motion is done using linear kinematics and therefore forces us to introduce concepts such as displacement, velocity, and acceleration, which are all essential in the branch of physics known as kinematics.

Motion In A Straight Line - Definition, Formulas, Examples, FAQs
Motion In A Straight Line

What is Motion?

Before we begin Motion in a Straight Line motion, let's first introduce 'what is motion'?. In our daily life, we are surrounded by moving objects. For example: Walking on the streets, a running boy, etc. The above movements of the objects are examples of motion.

Motion: The change in the position of any object with respect to time is called motion.
Kinematics: The study of the motion of an object without knowing its cause is called kinematics.

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What is Straight-Line Motion?

Movement is a phenomenon in which an object over time changes position. In terms of movement, distance, speed, acceleration along with time, motion is described quantitatively. In the field of physics that describes the motion of objects but does not refer to the source of objects is called kinematics.

Motion in Straight Line Formulas

Three motions in straight-line formulas are as follows:

1. $\mathrm{v}=\mathrm{u}+\mathrm{at}$
2. $s=u t+0.5 a t^2$
3. $v^2=u^2+2 a s$

Define Linear Motion

Linear motion is the motion that is natural to an object: moving in a straight line. According to Newton's First Law of Motion, an object not affected by any force will continue indefinitely in a straight line. The position x, which varies with t, can be used to explain the motion of a particle (a point-like object) down a line (time). An athlete running 100 metres on a straight track is an example of linear motion. Motion along a straight line is called linear motion.

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Types of Linear Motion

Linear motion, also called Rectilinear Motion can be of two types:
1. Uniform linear motion with constant velocity or zero acceleration
2. Non-uniform linear motion with variable velocity or non-zero acceleration

Movement in a straight line is literally one-dimensional and is simplest. Based on the first law of Newton, this says that an object will remain at rest or continue in straight motion at a uniform speed until an external force does not act upon it.

Do not confuse linear motion with general motion, because as we've mentioned, linear motion is one-dimensional. But in general, it has both a magnitude and direction, such that we describe an object's position and velocity in vector quantities.

Uniform Motion in a Straight Line

if a body moves along a straight path and at regular intervals of time it travels equal distances, it is said to have uniform motion. Simply put, uniform acceleration in the body means that the rate of change of velocity is constant.

Example:
If a car travels at a speed of $60 \mathrm{~km} / \mathrm{hour}$, it will cover a $1 \mathrm{~km} /$ minute. In this sense, the motion of car acceleration is uniform.

Non-uniform Motion in a Straight Line

In contrast to uniform acceleration, a body is said to exhibit non-uniform motion when it has unequal changes in velocity over equal intervals of time - that is, the rate of change of velocity differs at different time points during its motion.

Example:
A boy is kicking a football. It might cover 4 meters in the first attempt, 6 meters in the second change, 9 meters in the third attempt and so on as per the velocity exerted by the boy.

Frequently Asked Questions (FAQs)

Q: What is the role of friction in real-world linear motion scenarios?
A:
Friction is a force that opposes the relative motion of objects in contact. In real-world linear motion, friction can cause objects to slow down (like a car braking) or prevent motion altogether (static friction). Friction complicates the equations of motion because it introduces a force that depends on the nature of the surfaces in contact and the normal force between them. Understanding friction is crucial for accurately predicting and analyzing motion in practical situations.
Q: How does the concept of centripetal acceleration relate to linear motion?
A:
Centripetal acceleration is the acceleration directed towards the center of a circular path, causing an object to move in a circle. While it's not directly part of linear motion, understanding centripetal acceleration helps explain why objects don't continue in a straight line when moving in a circle. It's the presence of this acceleration that causes deviation from straight-line motion.
Q: What is the difference between distance and displacement in circular motion compared to linear motion?
A:
In linear motion, distance and displacement can be equal if the motion is in one direction. However, in circular motion, they are always different. The distance traveled in circular motion is the length of the arc, while the displacement is the straight-line distance between the start and end points. After one complete revolution in circular motion, the distance traveled is the circumference of the circle, but the displacement is zero.
Q: How does the concept of work relate to motion in a straight line?
A:
Work is done when a force acts on an object and causes a displacement in the direction of the force. In straight-line motion, work is calculated as the product of the force and the displacement in the direction of the force. Understanding work is important because it relates to energy transfer and can help in analyzing the causes and effects of motion.
Q: What is the significance of the acceleration due to gravity (g) in vertical motion problems?
A:
The acceleration due to gravity (g), approximately 9.8 m/s² near Earth's surface, is crucial in vertical motion problems. It represents the constant acceleration experienced by objects in free fall or vertical projectile motion (neglecting air resistance). This constant acceleration allows us to use the equations of motion to predict the position and velocity of objects at different times during their vertical motion.
Q: What is the relationship between displacement, velocity, and acceleration in straight-line motion?
A:
In straight-line motion, velocity is the rate of change of displacement with respect to time, and acceleration is the rate of change of velocity with respect to time. Mathematically, velocity is the first derivative of displacement with respect to time, and acceleration is the second derivative of displacement or the first derivative of velocity with respect to time.
Q: How does the concept of momentum relate to motion in a straight line?
A:
Momentum is the product of an object's mass and velocity. In straight-line motion, momentum is a vector quantity pointing in the direction of motion. The concept of momentum is important because it is conserved in collisions and interactions, providing a powerful tool for analyzing complex motions and predicting outcomes of interactions between objects.
Q: What is the relationship between average velocity and instantaneous velocity?
A:
Average velocity is the displacement divided by the time interval for a given period, while instantaneous velocity is the velocity at a specific moment in time. Instantaneous velocity can be thought of as the limit of average velocity as the time interval approaches zero. In a velocity-time graph, average velocity is represented by the slope of the secant line, while instantaneous velocity is the slope of the tangent line at a point.
Q: How does air resistance affect the equations of motion for straight-line motion?
A:
Air resistance introduces a force that opposes motion and typically increases with speed. This makes the equations of motion more complex, as acceleration is no longer constant. With air resistance, objects tend to reach a terminal velocity where the air resistance force balances the driving force (like gravity for falling objects). This results in motion that deviates from the simple equations used for motion in a vacuum.
Q: What is the physical meaning of the area under a speed-time graph?
A:
The area under a speed-time graph represents the distance traveled by the object. This is because distance is the product of speed and time, which is exactly what the area under this graph represents. For non-uniform motion, the total distance can be found by calculating the area under the entire curve.