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Motion in a straight line refers to the motion of a body without changing its direction.
- It is also known as linear motion or rectilinear motion.
- Motion is termed as the change in the position of an object over a specific period of time with respect to its surroundings.
- Mathematically, motion is described with reference to distance and displacement, velocity, acceleration, speed, and time.
- It is measured with respect to a certain frame of reference.
- It is also known as motion in one dimension, as the motion is in a certain straight direction.
- Kinematics is the study of motion independent of any potential forces or energies.
- Motion pertains to a variety of physical systems, including things, matter, particles, radiation as well as curvature, and space-time.
Read More: Potential Energy
| Table of Content |
Key Terms: Motion, Displacement, Velocity, Acceleration, Speed, Time, Distance, Linear Motion, Uniform and Non-Uniform Motion, Straight Line, Retardation, Equations of motion
What is Motion in a Straight Line?
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Motion in a straight line is a one-directional motion.
- It is also known as a linear or rectilinear motion.
- This motion can be measured through the use of a longitudinal dimension.
- Motion in a straight line is one of the foundational motions that exist.
- According to Newton’s first law of motion, a body without any net force on it continues to move in a straight line with a uniform velocity until and unless the body is subjected to a net force.
- External forces such as gravity and friction lead to a change in the object’s direction of motion.
Examples of Motion in a Straight Line
The following are the examples of motion in a straight line
- A moving car in a straight road
- Vertically falling raindrops
- Free fall of any object
- Falling fruits from trees
- A ball rolling down a ramp
- A train travelling on a straight track
- Up and Down lifting
- Rockets launch
Read More: Relative velocity
Motion in a Straight Line Video Explanation
Types of Linear Motion
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Linear motion is also known as motion in a straight line. Linear motion can be classified into two types which are:
- Uniform Motion
- Non-Uniform Motion
The uniform motion has zero acceleration and constant velocity while the non-uniform motion has non-zero acceleration and varying velocity.
The motion of an object with time varies.
Examples of Rectilinear or Linear Motion
Uniform Motion
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A body is said to be in uniform motion if it travels in a straight direction and covers equal distances in equal intervals of time.
- It has uniform acceleration which means the rate of velocity change remains constant for that object.
- For example, a car traveling at a speed of 60 km/h covers a distance of 1 km in a minute.
- Hence, the acceleration of the car is termed uniform.
Read More: Application and Uses of Convex Mirror, Examples
Non-Uniform Motion
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The motion of the body is said to be in non-uniform motion if it covers an unequal amount of distances in equal intervals of time.
- It has non-uniform velocity.
- During the movement of a body in non-uniform motion, its rate of change of velocity varies at different time periods.
- For instance, a car on a journey travels 4 km in the first hour, 6 km in the second, and 3 km in the third.
- Hence, it has a non-uniform motion.
Uniform and Non-uniform motion
Motion in a Straight Line Formulas
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The following are the formulas used in motion in a straight line. These are also known as Equations of motion
| Equations of Motion |
|---|
| \(v=u+at\) |
| \(S=ut+\frac{1}{2}at^2\) |
| \(v^2-u^2=2aS\) |
Where
- v is the final velocity of the body
- u is the initial velocity of the body
- a is the constant acceleration
- S is the distance covered by the body
- t is the time
Read More:
| Related Topics | |||
|---|---|---|---|
| Effects of Force | Balanced Force | Pseudo Force | |
| Work | Mass and Momentum | Impulse Formula | |
Things to Remember
- Motion in a straight line is widely referred to as linear motion.
- Motion is termed as the change in the position of an object over a specific period of time with respect to its surroundings.
- Linear motion can be classified into two types which are uniform and non-uniform motion.
- A body is said to be in a uniform motion if the body travels in a straight line while covering equal distances in equal time intervals.
- If a body covers unequal distances in equal time intervals, it is said to be in a non-uniform motion.
- For motion in a straight line, the formulas can be written as
- v = u + at
- s = ut + ½ at2
- v2 = u2 + 2as
Read More: Unit of Frequency
Previous Years’ Questions
- The time taken by her to walk up on the moving escalator will be…..[KCET 2020]
- A particle starts from origin O from rest and moves with a uniform… [JEE Main – 2019]
- In a car race on a straight road, car A takes a time t less than… [JEE Main – 2019]
- The maximum instantaneous velocity of the particle is around the point….[KCET 2018]
- Which graph corresponds to an object moving with a constant negative… [JEE Main – 2017]
- A car is standing 200m behind a bus, which is also at rest… [JEE Main – 2017]
- A body falls freely for 10sec. Its average velocity during this journey (take g=10ms−2)….[KCET 2016]
- A body is traveling towards East with a speed of… [JKCET – 2015]
- It travels a distance x1 in the first half of time and x2 in the next half of time, then….[KCET 2014]
- What is the average speed of the car ?...[KCET 2014]
Sample Questions
Ques. What is linear motion? (2 Marks)
Ans. Motion is a change in the position of an object over a specific period of time with respect to its surroundings. It can mathematically be described with reference to distance, displacement, velocity, acceleration, speed, and time. It is measured with respect to a certain frame of reference. Motion in a straight line is widely referred to as linear motion. It uses one dimension as the motion is in a certain straight direction only.
Ques. Why the instantaneous speed of an object is always equal to the instantaneous velocity’s magnitude? (2 Marks)
Ans. Instantaneous velocity refers to a particle’s velocity at a specific instant of time. In the case of a small-time interval, the displacement magnitude is effectively equal to the distance that is traveled by the particle in a same-time interval. Hence, no distinction is made between instantaneous velocity and speed.
Ques. Explain the types of Motion. (4 Marks)
Ans. There are various motions, some of which are as follows:
- Rotatory motion is the actual physical movement of an item that is spinning on its own axis. The motion is constant in all three directions.
- Oscillatory Motion, also known as periodic or oscillatory motion, is a repeating motion. Due to a restoring force or torque, the item in this motion oscillates in close proximity to its equilibrium position.
- Uniform circular motion is defined as an item moving at a consistent speed along a circular route.
- Rectilinear Motion is a straight line that forms the route of a linear motion in which the direction of the velocity does not change.
Ques. What is meant by Displacement? (1 Mark)
Ans. Displacement is the shortest possible path between the initial and final points.
Ques. State the differences between the two types of motion in a straight line. (3 Marks)
Ans. The difference between uniform and non-uniform motion are tabulated below:
| Uniform Motion | Non-Uniform Motion |
|---|---|
| A body is said to be in a uniform motion if the body travels in a straight line while covering equal distances in equal time intervals. | A body is said to be in a non-uniform motion if the body travels unequal distances in equal time intervals. |
| It has uniform acceleration which means the rate of velocity change remains constant for that object. | It has non-uniform velocity. |
| For instance, a car traveling at a speed of 60 km/h covers a distance of 1 km in a minute. | For instance, a car on a journey travels 4 km in the first hour, 6 km in the second, and 3 km in the third. |
Ques. A car that moves along a straight highway with a speed of 126 km/h is halted within a 200 m distance. What’s the car’s retardation, and how long does it take for it to stop? (3 Marks)
Ans. u = 126 km/h
= 35 m/s
s = 200 m
v = 0
We know that,
v2-u2 = 2as
0 - 352 = 2a x 200
a = -3.06 ms-2
As, v = u + at
t = (0-35)/ – 3.06
= 11.4 sec
Ques. What are the three equations for motion in a straight line? (3 Marks)
Ans. The three important equations for motion in a straight line are:
- v = u + at
- s = ut + ½ at2
- v2 = u2 + 2as
Ques. Two trains A and train B have 400 m and moves on 2 parallel tracks with a uniform speed of 71 km/h in the same direction. Train A is ahead of train B. The driver of train B decides to overtake train A and accelerates the train by 1 ms-1. If after a time interval of 50 sec, the guard of train B brushes past the driver of train A. What is the original distance between the two trains A and B? (3 Marks)
Ans. Here the length of trains A and B = 400 m.
As the speed of both trains is in the same direction
u = 72 km/h = 20 m/s
Hence their relative velocity uBA = 0.
If the initial distance between the A and B train is s.
Then train B covers (s+11) distance = (s+800) m in t time = 50 s when uniformly accelerated with acceleration a = 1ms-2
s+800 = uAB x t x ½ at2
= 0 + ½ x 1 x 502
= 1250 m
s = 1250 - 800
= 450 m
Therefore, the initial distance between the guard of two trains = 450 + 800
= 1250 m
Ques. What is Acceleration? (1 Mark)
Ans. Acceleration is the term for the speed at which a velocity changes.
Ques. A jet airplane is traveling at 500 km/h. It ejects its combustion products at a speed of 1500 km/h relative to the plane. Determine the speed of the latter with reference to an observer standing on the ground. (5 Marks)
Ans. The velocity of the jet airplane with respect to the observer standing on the ground = 500 km/h
If vj refers to the jet’s velocity and v0 refers to the velocity of the observer, then
vj–vo = 500 km/h
In the same way, if vc refers to the velocity of the products of combustion with respect to the plane, then
vc–vg = -1500 km/h
The negative sign depicts that the products of combustion move in an opposite direction to that of the jet.
Hence, the speed of combustion products with respect to the observer on the ground is:
= vc–u0 = (vc–vj) + (vj–v0)
= (-1500 + 500) km/h
= -1000 km/h
Ques. Define Retardation? (2 Marks)
Ans. When the speed of a particle decreases or when the particle slows down, the motion is said to be under retardation.
Ques. Define frame of reference. (2 Marks)
Ans. A frame with respect to which an observer observes the position and motion of an object is known as a reference frame.
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