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Motion in One Dimension – Acceleration

Acceleration        

It is defined as the rate of change of velocity and it is a vector quantity

(i)    Instantaneous acceleration :

It is defined as the acceleration of a body at some particular instant. Instantaneous acceleration

= \displaystyle \underset{\Delta t\to 0}{\mathop{\lim }}\,\displaystyle \frac{\Delta \overset{\to }{\mathop{v}}\,}{\Delta t}  = \displaystyle \frac{d\overset{\to }{\mathop{v}}\,}{dt}

(ii)   Average acceleration :  

\displaystyle {{\vec{a}}_{av}}= \displaystyle \frac{\Delta \overset{\to }{\mathop{v}}\,}{\Delta t} = \displaystyle \frac{\overset{\to }{\mathop{{{v}_{2}}}}\,-\overset{\to }{\mathop{{{v}_{1}}}}\,}{{{t}_{2}}-{{t}_{1}}}

The direction of average acceleration is the direction of the change in velocity vector
i.e. ­­ Δ\displaystyle \overset{\to }{\mathop{v}}\,

(iii)  Uniform acceleration :

A body is said to have uniform acceleration if magnitude and direction of the acceleration remains constant during particle motion.

Note :If a particle is moving with uniform acceleration, this does not necessarily imply that particle is moving in straight line.

Example : Two dimension projectile motion(parabolic path).

 (iv)  Non-uniform acceleration :  

 A body is said to have non-uniform acceleration, if it’s magnitude or direction or both, change during motion.

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