INSTANTANEOUS ACCELERATION
The acceleration of a particle at a particular instant of time is called it's instantaneous acceleration.
It is also defined as the limit of average acceleration as the time interval (\(\Delta t\)) becomes infinitesimally small.
If the time interval At is chosen to be very small, i.e., as \(
\Delta t \to 0
\), the corresponding acceleration is called instantaneous acceleration.
\(
\mathop {\lim }\limits_{\Delta t \to 0} \frac{{\Delta V}}
{{\Delta t}} = \frac{{dV}}
{{dt}}
\) =instantaneous acceleration
Note : Instantaneous acceleration
\(
a = \frac{{dv}}
{{dt}} = \frac{{d^2 s}}
{{dt^2 }};dv = _{t_1 }^{t_2 }
\) ad
Note \(
a = \frac{{dv}}
{{ds}}.\frac{{ds}}
{{dt}};
\) a=v.\(
\frac{{dv}}
{{ds}}
\) ;a.ds=v.dv (ds/dt=v)
DECELERATION OR RETARDATION
If the speed is decreasing with time then acceleration is negative.
The negative acceleration is called deceleration or retardation.
UNIFORM ACCELERATION
If the average acceleration over any time interval equals the instantaneous acceleration at any instant of time then the acceleration is said to be uniform or constant. It does not vary with time.
The velocity either increases or decreases at the same rate throughout the motion. (or)
If a body has equal changes in velocities in equal intervals of time however small the intervals may be, then it is set to move it uniform acceleration.