EQUATIONS OF MOTION
Equation of uniformly Accelerated motion:
Let the initial velocity of a body be ‘u’.
It is subjected to a uniform acceleration ‘a’ after time ‘t’. let the final velocity ‘v’.
Now acceleration = .
Or Acceleration =
So,
Or at = v – u
Or v = u + at
This is the first equation of motion.
It is used to find out the velocity ‘v’ acquired by a body in time ‘t’.
.
It gives the distance travelled by a body in time ‘t’.
Let a body has an initial velocity ‘u’
and a uniform acceleration ‘a’ for time ‘t’
So that it’s final velocity is ‘v’.
Average velocity = .
So, Average velocity =
Also, Total distance travelled = Average velocity × Time
[∵ Average velocity = ]
So,
(by putting the value of ‘v’ from first equation).
Or
Where s = distance travelled by the body in time ‘t’
u = Initial velocity of the body
and a = Acceleration
This is the second equation of motion.
The third equation of motion is v2 = u2 + 2as
s = ut + at2 …. (1)
From the first equation of motion, we have
v = u +at …. (2)
From (1) and (2)
at = v – u
Or …. (3)
Substituting the value of ‘t’ in equation (1),
This is the third equation of motion.
Where
v = final velocity
u = Initial velocity
a = acceleration and
s = distance travelled
This equation gives us the velocity acquired by a body in traveling a distance s.
Points to remember: