(a) Acceleration: It is defined as the ratio of change in velocity & the corresponding time taken by the mirror object i.e.
(i) It is vector quantity
(ii) It is either positive or negative.
(iii) Negative acceleration is called retardation.
(iv) Unit-m/s2 in SI & cm/s2 in CGS system. (v) Dimensional formula – [LT-2 ].
(b) Average acceleration: When an object is moving with a variable acceleration, then the average acceleration of the body is defined as the ratio of the total change in velocity during motion to the total time taken, i.e.
Average acceleration = \(\frac{Total \,change \,in \,velocity}{Total \,time\, taken}\)
(c) Uniform acceleration: An object is said to be moving with a uniform acceleration if its velocity changes by equal amounts in equal intervals of time.
(d) Instantaneous acceleration:
(i) If a body is moving with a variable acceleration, then the acceleration of a body at the given instant of time is called instantaneous acceleration.
(ii) If at an instant t, a body while moving with a variable acceleration shows a change in velocity ∆\(\vec v\) in a small interval of time ∆t, so that ∆t →0, then
Instantaneous acceleration = \(\lim\limits_{\Delta t \to 0}\frac{\vec {\Delta v}}{\Delta t}=\frac{\vec{d v}}{dt}\)
where, \(\frac{\vec {d v}}{dt}\) is the derivative of velocity (\(\vec v\)) w.r.t. time.
