Acceleration
ACCELERATION
If the velocity of a particle is changing as it moves then it is said to be moving with acceleration The acceleration measures how rapidly the velocity is changing.
Acceleration is defined as the rate of change of velocity.
\(
\therefore \mathop {a = \lim }\limits_{\Delta t \to 0} \frac{{\Delta V}}
{{\Delta t}} = \frac{{dV}}
{{dt}}
\)
The average acceleration is defined as the ratio of change in velocity over a time interval to the time interval.
Average acceleration= \(
\frac{{\mathbf{change}\text{ }\mathbf{in}\text{ }\mathbf{velocity}}}
{{\mathbf{time}\text{ }}}
\)
\(
\therefore a = \frac{{V_2 - V_1 }}
{{t_2 - t_1 }} = \frac{{\Delta V}}
{{\Delta t}}
\)
It is a vector. It is in the direction of change in velocity.
S.I. Unit is \(
ms^{ - 2}
\), dimensional formula is [\(
L^1 T^{ - 2}
\)]
Note : The velocity variation may be due to change in magnitude of velocity (speed) or change in direction of velocity. Hence acceleration may be due to either of the above reasons or both.
Eg 1: For a car going on a straight road if the speed is increasing, then the acceleration is due to change in magnitude of velocity
Eg 2: For a stone whirled in a horizontal circle with constant speed, the acceleration is due to change in direction of velocity.
Eg 3: For a stone whirled in a vertical circle with a changing speed, the acceleration is due to change in both magnitude and direction of velocity.
Note : The acceleration of a moving particle may be positive or negative. If the speed of particle is increasing with time then acceleration is positive and if the speed is decreasing with time then acceleration is negative.
This statement is independent of the choice of reference axis
Note : For positive acceleration the velocity vector and acceleration vector are in the same direction. But for negative acceleration, the velocity and acceleration vectors are opposite.