Acceleration can be defined as the rate of change of velocity with time. The unit of acceleration is ms-2. It is also the increase in velocity per unit time. $${Acceleration (a)} = \frac{∆v}{t} $$ $${Acceleration(a) } = \frac{v - u} {t} $$ $${where} $$ $${v} = \text{final velocity} $$ $${u} = \text{initial velocity} $$
This can be defined as the decrease in velocity per unit time. A car about to be parked can be said to undergo deceleration or retardation.
When an object is travelling in a straight line with an increase in velocity at equal intervals of time, then the object is said to be in uniform acceleration. Free falling of an object is an example of uniform acceleration
This can be defined as the rate of change of velocity at any instant in time. $${a} = \frac{∆v}{∆t} \text{ lim ∆t —>0}$$
The equation of a body that undergoes uniform acceleration in a rectilinear path is given as follows: $$ a = \frac{v - u} {t} $$ $$\text{cross multiplying} $$ $${v - u } = at $$ $${v} = {u + at} \text{ .....(1) }$$ $$But, $$ $$\text{Average velocity} =\frac{v - u}{2} $$ $$\text{substituting V = u + at in eqn 1} $$ $$\text{average velocity} = \frac{u + u + at} {2} $$ $$ = \frac{2u + at} {2} $$ $$= \frac{2u}{2} + \frac{at}{t} $$ $$ = {u} + \frac{1}{2}at² $$ $${But, } $$ $${Velocity} = \frac{s}{t} $$ $$\frac{s}{t} = u + \frac{1}{2}at $$ $$\text{cross multiplying} $$ $${s} = t(u + \frac{1}{2}at) $$ $${s} = ut + \frac{1}{2}at² \text{ ....(2)} $$ $$\text{squaring equation 1} $$ $${v²} = {(u + at)}² $$ $${v²} = {u² + 2uat + a²t²} $$ $${v²} = {u²} + 2a {(ut + \frac{1}{2}at²)} $$ $$\text{sub s = }ut + \frac{1}{2}at² \text{ in the expression} $$ $${v²} = {u² + 2as} \text{ ....(3)} $$ Equations of motion are given as thus:
Note: When a body starts from rest u = 0
When a body comes to rest of stops moving v = 0
When a body moves at uniform speed a = 0
The equations of motion are also called the equations of kinematics.