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Motion is described as the change in position or the change in environment with respect to time. Any motion in the universe must be one of the following motions. If not, it must be a resultant movement of the following motions.

  1. Linear motion
  2. Angular motion
  3. Simple harmonic motion

Linear motion or Rectilinear motion is the motion of an object along a straight line.

E.g –

  • A fruit falling from a tree
  • Motion of a vehicle on a straight road

Physical quantities related to the linear motion

Physical quantities that are related to linear motion are

  • Distance,
  • Linear displacement,
  • Speed,
  • Linear velocity,
  • Linear acceleration,

and etc.

Distance (d)

The length of a path traveled by an object is called distance. The SI unit of distance is meters (m). Distance is a scalar.

Example 01

A ball is shot vertically upwards from the top of a building 80m high. The ball travels 10m vertically up and reaches the ground. Find the distance traveled by the ball.


Linear Motion eq 01

Speed (V)

Speed is the rate of change in distance. If an object travels "S" distance within "t" time, the speed of the object can be written as follows.

Linear Motion eq 02

Example 02

A vehicle is traveling at the speed of 108 kmh-1.

  1. Find the speed in meters per second (ms-1)
  2. Find the distance traveled at 10 seconds.
  3. Find the time that takes to travel 1500m.


part 1

Linear Motion eq 03

part 2

Linear Motion eq 04

part 3

Linear Motion eq 05

Example 03

Two objects A and B start to move at the same position in the same direction with the velocities of 4 ms-1 and 6 ms-1 respectively. Find the time taken for the distance between the two to be 30 m.


Linear motion question 01

Let's take the time taken for the distance between A and B to be 30 m as "t". At the time "t" if object A, traveled distance x, object B has traveled x+30.

Linear Motion eq 06

For object  A,

Linear Motion eq 07

For object B,

Linear Motion eq 08

Example 04

A bat flies towards a wall 10m away with a speed of 20 ms-1. The sound waves produced by the bat hit the wall and the bat hears an echo. If the speed of sound waves in air is 330 ms-1, what is the distance between the bat and the wall when the echo is heard?


Linear motion question 02

Let's take the distance traveled by the bat as "x" and the time is "t" when it hears the echo.

Linear Motion eq 09

The distance should be traveled by the sound wave at the time "t",

Linear Motion eq 10

Average speed

When an object changes its speed during the movement, we calculate the average speed for the entire movement.

Linear Motion eq 11

Example 05

A car traveling non-stop from city A to city B covers the first 200 km in 4 hours and the remaining 400 km in 5 hours. Find the average speed of the car.


Linear Motion eq 12

Example 06

A bird flying up a hill travels 1.8 km in 9 seconds. The rest travel at a speed of 15 km h-1 in five minutes. Find the average speed of the bird.


Linear Motion eq 13

Example 07

A motorcycle travels from A to B. Half of the journey is at a speed of 50 km h-1 and the other half at a speed of 30 km h-1. Find the average speed of the motorcycle.


Let's take the total travel distance as "2x". Therefore, the halfway would be "x". Let's take the times taken to travel first half and second half are t1 and t2 respectively.

Linear Motion eq 14

Linear displacement (d)

Displacement is the shortest distance between two points. Displacement is a vector.

Example 08

A car travels 20 km towards the east and then 12 km north. It again travels 14 km to the west and then travels 4 km to the south and stops. Find the displacement of the car.

Linear motion question 03
Linear Motion eq 15

Linear velocity (V)

Linear velocity is the rate of the change of the linear displacement. Linear velocity is also a vector.

Linear Motion eq 16

Average velocity

 If an object changes its velocity, we calculate the average velocity. If an object starts to move with the velocity of "U" and, after time "t" the object obtains a velocity "V" the average velocity can be written as follows.

Linear Motion eq 17

Resultant velocity

When an object has multiple velocities, we should calculate the resultant velocity. If two velocities act in the same direction, the resultant velocity would be the sum of the velocities. If two velocities act in opposite directions, the resultant velocity would be the difference in velocities. If there is another angle between velocities, we can use the parallelogram law to find the resultant velocity

Parallelogram law
Figure 04: Parallelogram law

Linear Motion eq 31

Example 09

A train is moving at a speed of 240 km h-1 on a straight railway track. Find the displacement taken at 5 minutes. What is the time taken to travel 1200 km at this speed?


Linear Motion eq 18

Time taken to travel 1200 km,

Linear Motion eq 19

Example 10

When two cars (A and B) move in the same direction, they approach each other by 4 meters in 1 second. When the two cars move in opposite directions, they move away from each other by 2m in 1 second.


Let's take the velocities of A and B are VA and VB.

Linear Motion eq 20

Linear acceleration (a)

Linear acceleration is the rate of change of velocity of an object that is in a linear motion. If the acceleration is decreasing with time, it is a negative acceleration. Negative acceleration is commonly known as "Retardation" or "De-acceleration". Linear acceleration is a vector. If an object starts a linear motion with a velocity of "V" and after time "t" it obtains velocity "V", the acceleration can be written as follows,

Linear Motion eq 21

Example 11

An object moving on a straight line takes 10 seconds to obtain 60 ms-1 velocity from 10 ms-1 velocity. Find the linear acceleration, Average velocity, and Displacement of the object.


Linear acceleration

Linear Motion eq 22

Average velocity,

Linear Motion eq 23

Linear displacement,

Linear Motion eq 24

Example 12

An object with an acceleration of 8 ms-1 acquires a velocity of 40 ms-1 in 4 seconds. Find the initial velocity, Average velocity, and Displacement of the object within 4 seconds.


Initial velocity,

Linear Motion eq 25

Average velocity,

Linear Motion eq 26

Displacement within 4 seconds,

Linear Motion eq 27

Example 13

The velocity of a bullet that travels toward a wooden block is 220 ms-1.  After the bullet hits the wood, it sinks into the wood and decreases its velocity to 20 ms-1 within 0.2 seconds. Find the de-acceleration and the displacement taken place by the bullet at 0.2 seconds.



Linear Motion eq 28


Linear Motion eq 29

Motion equations

We can use the following equations to solve problems associated with motion. But these equations are only valid for linear motion and if there is an acceleration, it should be constant.

Linear Motion eq 30


  • S = Linear displacement
  • U = Initial velocity
  • V = Final velocity
  • a = Linear acceleration
  • t = Time

Next learn about another important concept of mechanics, Linear momentum.

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References and Attributes


The cover image was designed using an image by Wuestensohn2000 from Pixabay

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