Equations of Uniformly Accelerated Motion

We have about three equation of linear motion introduced by sir Isaac Newton’s in 1886, include the following

i)       Newton’s first equation of motion

ii)     Newton’s second equation of motion

iii)   Newton’s third equation of motion

FIRST EQUATION OF MOTION

It is related final velocity, initial velocity, acceleration and time taken. The Newton’s first equation of motion is given by:

v = u + at

 Consider a body with initial velocity (u), acceleration (a) for a time (t) and final velocity (v)

 

SECOND EQUATION OF MOTION

It relates distance (displacement) moved, initial velocity,  time taken, and acceleration. The Newton second equation is given by:

  S = ut + ½(at²) 

 Consider the Distance = Average velocity x Time

                                 Then;

THIRD EQUATION OF MOTION

It relates to final velocity, initial velocity, acceleration and distance moved.  The Newton’s third equation of motion is given by

v² = u² + 2as

Consider the first equation v = u + at

Hence the three equations of motion are

i)       v = u + at

ii)     s = ut + ½at²

iii)   v² = u² + 2as

   

Example 1

A body moving at 10 m/s accelerates uniformly at 2 m/s² for 8 seconds. Determine the final velocity.

Solution

Data given

Initial velocity (u) = 10 m/s

Acceleration (a) = 2 m/s²

Time (t) = 8 s

Final velocity (v) =?

The final velocity of the body = 26 m/s

Example 2

A body moving with a velocity of 30 m/s is accelerated uniformly to a velocity of 50 m/s in 5 seconds.

Calculate;

a)      Acceleration of the body

b)      The distance travelled by the body

Solution

Data given

Initial velocity (u) = 30 m/s

Final velocity (v) = 50 m/s

Time (t) = 5 s

Acceleration (a) =?

Distance (s) =?

a)      Acceleration,

The acceleration of the body = 4 m/s²

 b)      The distance travelled;

The distance travelled by the body = 200 m

  

Example 3

A body moving with a velocity of 5 m/s accelerates at 2 m/s² and covers a distance of 15 m. Determine the final velocity just when covering the distance.

Solution

Data given

Initial velocity (u) = 5 m/s

Acceleration (a) = 2 m/s²

Distance (s) = 15 m

Final velocity (v) =?

 

The final velocity of the body = √85 m/s