Newton’s first law of motion

In order for an object to accelerate it needs to be acted upon by a force. As we have seen in an earlier post on acceleration.

From the post on acceleration we can deduce that there are four changes that can take place if a force acts on an objects:

1. The speed of the object will increase from zero if it was at rest and the object will move in the direction in which the force is acting.
2. The speed of the object will increase if the force is acting in the same direction as the the direction of motion of the object until the force no longer acts on the object.
3. The speed of the object will decrease if the force is acting in a direction opposite to the direction of motion of the object. The speed of the object might decrease to zero if the force acts for long enough.
4. If the object is moving and the force is acting in a direction perpendicular to the direction of motion of the object then the object will move in a circular path. When the application of the force stops the object will leave the circular path and would move in a straight line in a direction tangential to the circular path.

These four changes can be combined together to produce the Newton’s first law of motion as shown below:

Unless a force is applied an object will continue in its state of rest or uniform motion in a straight line.

Another way to write this law:

If a force is applied (i) an objects that was at rest will no longer be at rest or (ii)if moving with a uniform  will no longer have a uniform or constant speed or lastly (iii) if moving in a straight line will no longer move in  the same direction

This law is thus explaining that if a force is acting on an object then the object will experience an acceleration. However we are officially learn this only when we see the Newton’s second law of motion.

First equation of motion

The first equation of motion is mainly derived from the definition of acceleration.

You would remember that acceleration is the rate of change of velocity with time  and that the equation to calculate it is

acceleration = (change in velocity)/time taken

                    = (final velocity – initial velocity) /time taken

           a  = (v_f – v_i)/t

Rearranging the equation will give you

v_f = v_i + a*t

In some books the equation is given as such

v = u + at

If we used the equation above then the symbol v will be the final velocity and the symbol u will be the initial velocity of the object.

Now as we have seen in this post on acceleration if the final velocity is greater than the initial velocity then the acceleration is positive but if the initial velocity is greater than the initial velocity then the acceleration is negative.

Now let us have a look at two examples on the first equation of motion.

Example 1

A boy starts from rest accelerate to a velocity of 10 m/s in a time of 10 s. Determine the acceleration of the boy.

His final velocity v = 10 m/s

His initial velocity u = 0 m/s since he started from rest.

Time taken t = 10 s

Using the equation v = u +at and making  a the subject of formula will give you a = (v-u)/t

Substituting the different values of v, u and t in the equation will give you

a = (v-u )/t

  =(10 – 0 ) /10

  = 1 m/s²

Example 2

A train travelling at a speed of 100 m/s is decelerated to a speed of 50 m/s in a time of 15 s. Calculate the deceleration that the train is subjected.

final velocity v = 50 m/s

initial velocity u = 100 m/s

time taken t = 15 s

using the equation v = u +at and making a the subject of formula will give you the equation

a = (v-u) /t

Substituting in the equation above the different values of v, u and t

a = (v-u)/t

   = (50 –100 )/15

  = –50 /15

= - 3.33 m/s²

Since the acceleration is – 3.33 m/s² then

deceleration  = 3.33 m/s²