Rectilinear motion refers to the motion of an object along a straight line. In rectilinear motion, the object's position changes with respect to time, but its path remains linear, following a single dimension.
This article discusses rectilinear motion, its characteristics, equations, types, laws, differences from linear motion, and frequently asked questions.
Table of Content
What is Rectilinear Motion?
Rectilinear motion describes the movement of an object in a straight line, without any deviation or change in direction. It involves motion solely along one dimension, such as horizontally, vertically, or along an inclined plane. This type of motion is characterized by constant speed or acceleration along the linear path.
Rectilinear motion is commonly encountered in various real-world scenarios, from the motion of vehicles along roads to the descent of objects under gravity.
Definition of Rectilinear Motion
Rectilinear motion is the movement of objects in a straight-line regardless of its path
Displacement
Displacement is a vector quantity that describes the change in position of an object moving from one point to another. It is defined as the straight-line distance and direction from the initial position of the object to its final position.
Speed
The speed is the "how fast something moves", shown as the time needed to cover a distance. It tells you how rapidly an item is moving through a space. As such as your car is driving 60 mile in one hour you may conclude your speed is 60 miles per hour (mph).
Examples of Rectilinear Motion
- A car moving along a straight road.
- A train traveling along a straight track.
- A bullet fired from a gun in a vacuum.
- A person walking in a perfectly straight line.
- A rocket ascending vertically before reaching escape velocity.
Characteristics of Rectilinear Motion
Straight Path: The Object moves on a line that is straight without any deviation.
Constant Speed or Uniform Motion: The object moves along a straight line with a uniform speed, covering equal distances in equal time-intervals.
Direction: The motion can be in any direction. It can be either along the straight line or it can be perpendicular to it.
Absence of External Forces: In the best case (for example, in vacuum there are no forces acting on the object which would affect its motion), there are no external forces which change its motion, but, forces like friction must be considered.
Equations of Motion for Rectilinear Motion
In rectilinear motion, the equations of motion are derived from Newton's laws of motion and describe the relationships between position, velocity, acceleration, and time. Here are the three basic equations of motion for rectilinear motion:
First Equation of Motion
This equation relates the final velocity (v) of an object to its initial velocity (u), the acceleration (a) experienced by the object, and the time (t) taken for the motion to occur.
v = u + at
Second Equation of Motion
This equation relates the displacement (s) of the object to its initial velocity (u), the acceleration (a) experienced by the object, and the time (t) taken for the motion to occur.
s = ut + (1/2)2
Third Equation of Motion
This equation relates the final velocity squared (v2) of the object to its initial velocity squared (u2), the acceleration (a) experienced by the object, and the displacement (s) of the object.
v2 = u2 + 2as
Types of Rectilinear Motion
Some types of rectilinear motion are discussed below:
Uniform Rectilinear Motion
Uniform rectilinear motion occurs when an object moves along a straight path with constant velocity. In other words, the object covers equal distances in equal intervals of time.
Characteristics of Uniform Rectilinear Motion
- Constant velocity: The object moves with a constant speed and direction.
- Linear path: The motion occurs along a straight line.
- No acceleration: Since velocity remains constant, there is no acceleration involved.
Example: A car traveling along a straight highway at a steady speed of 60 mph without any changes in its velocity or direction.
Non-uniform Rectilinear Motion
Non-uniform rectilinear motion occurs when an object moves along a straight path with a changing velocity. This means the object covers unequal distances in equal intervals of time.
Characteristics of Non-uniform Rectilinear Motion
- Changing velocity: The object's speed or direction changes over time.
- Variable acceleration: Since velocity changes, there is acceleration involved, which could be positive, negative, or zero.
- Linear path: Similar to URM, the motion still occurs along a straight line.
Example: A car initially accelerating from rest, gradually increasing its velocity as it travels along a straight road. The acceleration could be due to pressing the gas pedal.
Simple Harmonic Motion
Simple harmonic motion is a repetitive movement pattern where an object swings to and fro around a central point. This happens because of a force that pulls the object back towards its starting position whenever it moves away from there. This force gets stronger as the object moves farther away and weaker as it gets closer, always pushing the object back towards the middle.
Example, think of a mass connected to a spring. As it moves back and forth, the spring pulls it back to its starting point whenever it is pushed away. This repeats unless something interferes. Other examples include a clock's pendulum and a guitar string vibrating.
Difference Between Linear and Rectilinear Motion
The key difference between linear and rectilinear motion is given below:
Linear Motion | Rectilinear Motion |
|---|---|
Linear motion is defined as when a body is moving in a straight line or along a curved line in a plane. | Rectilinear motion is defined as a phenomenon in which a body is moving only along a straight line. |
Examples of Linear Motion are,
| Examples of Rectilinear Motion are,
|
It is along any curve line or straight line in a plane. | It is only along a straight line in a plane. |
It has non-zero acceleration. | It has zero acceleration. |
It is also called translation motion. | It is a type of linear motion. |
There are two types of linear motion.
| There are three types of Rectilinear Motion.
|
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Solved Examples on Rectilinear Motion
Example 1: A car accelerates uniformly from rest to a speed of 20 meters per second in 10 seconds. What is the acceleration of the car?
Solution:
Given, initial velocity (u) = 0 meters per second, final velocity (v) = 20 meters per second, time (t) = 10 seconds.
Using the formula for acceleration: Acceleration (a) = (final velocity - initial velocity) / time Acceleration
(a) = (20 m/s - 0 m/s) / 10 s
Acceleration (a) = 20 m/s / 10 s
Acceleration (a) = 2 meters per second squared
So, the acceleration of the car is 2 meters per second squared.
Example 2: A stone is thrown vertically upward with a velocity of 30 meters per second. How high does it go before it starts to fall back down? (Take acceleration due to gravity as 10 meters per second squared).
Solution:
Given, initial velocity (u) = 30 meters per second, acceleration due to gravity (g) = -10 meters per second squared (negative because it acts in the opposite direction to the motion).
Using the equation of motion: Final velocity (v) = 0 meters per second (at the highest point) v2 = u2 + 2as
So, 0 = (30 m/s)2 + 2(-10 m/s2)s
0 = 900 -20s
s = 900 / 20
s = 45 meters
So, the stone reaches a height of 45 meters before it starts to fall back down.
Example 3: A train accelerates uniformly from 10 meters per second to 30 meters per second in 5 seconds. What is its acceleration?
Solution:
Given, initial velocity (u) = 10 meters per second, final velocity (v) = 30 meters per second, time (t) = 5 seconds.
Using the formula for acceleration:
Acceleration (a) = (final velocity - initial velocity) / time
Acceleration (a) = (30 m/s - 10 m/s) / 5 s
Acceleration (a) = 20 m/s / 5 s
Acceleration (a) = 4 meters per second squared
So, the acceleration of the train is 4 meters per second squared.
Example 4: A ball is dropped from a height of 20 meters. What is its velocity just before hitting the ground? (Take acceleration due to gravity as 10 meters per second squared)
Solution:
Given, initial velocity (u) = 0 meters per second, acceleration due to gravity (g) = 10 meters per second squared, displacement (s) = -20 meters (negative because it is downward).
Using the equation of motion: v2 = u2 + 2as
So, v2 = 02 + 2(10 m/s2)(-20 m)
v2 = 0 + (-400 m2/s2)
v2 = -400 m2/s2
Since velocity cannot be negative, we take the magnitude: v = √(400 m2/s2) v = 20 meters per second
So, the velocity of the ball just before hitting the ground is 20 meters per second.