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Rectilinear motion, also known as linear motion, is the one-dimensional motion of an object along a straight line. According to the Newton’s first law of motion, any object in the absence of a net force will continue to move in a straight line only. In rectilinear motion, the motion of an object can be described by taking its position x, varying with the time (t). Some common examples of linear motion seen in everyday life includes an athlete running in a straight line, train moving on the track etc.
Motion, in physics, is described as the change in the position of an object with respect to the frame of reference and time. Depending upon the path followed by an object, its motion can be divided into different categories like rectilinear motion, projectile motion, rotational motion, angular motion etc.
Check Also: Motion in a Straight Line
Key Terms: Linear Motion, Newton’s Laws of Motion, Speed, Velocity, Uniform Motion, Non-Uniform Motion
What is Rectilinear Motion?
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Rectilinear motion is a kind of motion which can be described only through one axis. If there is no external force acting on an object, then the object will follow a straight path only. In a rectilinear motion, all the parameters of motion like distance, displacement, velocity etc. are in the same direction. Hence, the motion is called one-dimensional motion.
Distance and Displacement
Distance is defined as the total path length covered by a moving object or a particle during its motion. For example, if an object moves 10 km forward and 15 km in backward direction, then the total distance covered by the object is 10 + 15 = 25 km.
Whereas, displacement is the net distance covered by a moving object between its initial and final position. For example, an object moves 15 km forward and 10 km in backward direction, then the total displacement covered by the object is 15 - 10 = 5 km. This means that the object is 5 km away from the starting point.
Distance is always positive while displacement can be either positive or negative.
Speed and Velocity
Speed is the distance covered by an object per unit time. It is a scalar quantity and does not consider the direction of the moving object. It can be written as,
Speed = Distance / Time
Whereas, velocity of an object is the rate of change in its displacement. Velocity is a vector quantity that considers both the magnitude and direction of the moving object. It can be calculated using the formula,
Velocity = Displacement / Time
Or
Velocity = (Final Position – Initial Position) / Time
The speed of an object can never be negative, but the velocity can either be positive or negative. The negative sign indicates opposite direction.
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Examples of Rectilinear Motion
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Some examples of rectilinear motion are provided below:
- An athlete running on a track
- An object falling straight down
- A train moving on a straight track
- A man dropping a ball off a cliff
- A skydiver jumps out off a plane
- Hot water that falls into a tea cup from a vending machine
- Skateboarders going down an inclined path
- Any metallic particle in free fall, which is under the effect of gravitational forces
- Planes in the sky that moves along a straight path
- Kids sliding down on a slide
- The elevators used in public places
Types of Rectilinear Motion
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Rectilinear motion can be categorized into three types mentioned below:
- Uniform Rectilinear Motion – It is a type of rectilinear motion in which an object travels in a straight path with uniform speed and zero acceleration.
- Uniformly Accelerated Rectilinear Motion – In this type of rectilinear motion, an object travels with a constant acceleration along its path.
- Non-Uniformly Accelerated Rectilinear Motion – In this type, the speed and the acceleration of the moving object is non-uniform.
Difference Between Uniform Motion and Non-Uniform Motion
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Linear motion can be of two types – uniform and non-uniform. The key differences between uniform and non-uniform motion are tabulated below:
| Uniform Motion | Non-Uniform Motion |
|---|---|
| When the body covers equal distances in equal intervals of time, it is said to be in uniform motion. | When the body covers unequal distances in equal intervals of time, it is said to have non-uniform motion. |
| In this, the acceleration of the moving object is zero. | In this, the object has non-zero acceleration. |
| In uniform motion, the distance-time graph shows a straight line. | In non-uniform motion, the distance-time graph shows a curved line. |
Things to Remember
- Motion in a straight line is referred to as rectilinear motion or linear motion.
- A particle is said to be in uniform motion if the particle travels in a straight line while covering equal distances in equal time intervals.
- A particle is said to be in non-uniform motion if the particle tends to cover unequal distances in equal interval of time.
- The motion of two particles under the influence of electrostatic force can be determined as rectilinear motion.
- Rectilinear motion is of three types – uniform, uniformly accelerated, and non-uniformly accelerated.
Sample Questions
Ques. Why is rectilinear motion considered as a one-dimensional motion? (1 Mark)
Ans. In rectilinear motion, the motion of an object can be described in a single axis only, therefore, it is considered as a one-dimensional motion.
Ques. What is a non-uniform motion in a straight line? (1 Mark)
Ans. When an object covers unequal distance in equal interval of time while moving along a straight line, it is said to have non-uniform motion.
Ques. Why is the instantaneous speed of an object always equal to the instantaneous velocity’s magnitude? (2 Marks)
Ans. Instantaneous velocity is defined as the particle’s velocity at a specific instant of time. In case of a small time interval, the distance will be equal to the displacement magnitude which is travelled by particle in the same time interval. Hence, the instantaneous speed of a particle is always equal to its instantaneous velocity’s magnitude.
Ques. State the difference between rectilinear and curvilinear motion? (2 Marks)
Ans. Rectilinear motion occurs in a single dimension, therefore it is also known as motion in one dimension. It can also be called motion in a straight line.
Curvilinear motion occurs along a curve other than a straight line. Therefore, it can be called as two dimensional or three dimensional motion.
Ques. A body is moving with an initial velocity of 2 m/s and acceleration of 0.5 ms-2. Find the time when the velocity of the particle becomes zero. (2 Marks)
Ans. Final velocity, v = 0
v = u + at
0 = 2 – 0.5t
t = 4 s
Ques. Let the initial velocity of the particle is 5 m/s. It is accelerating at an acceleration of 1 ms-2. Its final velocity is 10 m/s, then what will be the distance travelled by this particle? (2 Marks)
Ans. We know, v2 = u2 + 2as
102 = 52 + 2 × 1 × s
s = 37.5 m
Ques. What are the different types of rectilinear motion? (3 Marks)
Ans. There are 3 types of rectilinear motion:
- Uniform rectilinear motion - In this motion, velocity is kept constant. There is no acceleration and no external force acting on the object.
- Uniform accelerated rectilinear motion - In this motion, velocity changes but acceleration is kept constant.
- Non-uniformly accelerated rectilinear motion - In this, neither velocity nor acceleration of the particle is kept constant. Both the quantities vary with time.
Ques. What are the different types of motion? (3 Marks)
Ans. There are 4 basic types of motion -
- Rotary Motion - It is a type of motion in which the particle rotates about a given fixed axis. For example - clock.
- Oscillatory Motion - It is a type of motion in which the particle repeatedly repeats the same motion again and again. For example - swing.
- Linear Motion - It is a one dimensional motion along a straight path. For example - a cyclist along a straight path.
- Reciprocating Motion - It is a type of motion having repetitive upward and downward or back and forth motion. For example - a needle in a sewing machine.
Ques. A car that moves along a straight highway with a speed of 126 km/h is halted within a 200 m distance. What is the car retardation, and how long does it take for it to stop? (5 Marks)
Ans. Initial velocity (u) = 126 km/h = 35 m/s
Distance (s) = 200 m
Final velocity (v) = 0
We know the third equation of motion,
v2 - u2 = 2as
0 - 352 = 2 × a × 200
a = -3.06 ms-2
According to first equation of motion, v = u + at
t = (0-35) / -3.06
t = 11.4 s
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