Acceleration Physics Notes
Acceleration:
Generally, the velocity of a moving object changes with time. Sometimes the magnitude of velocity increases and sometimes it decreases. Sometimes the magnitude remains constant but the direction changes as in circular motion. The rate of change in velocity is defined as acceleration.
Therefore, “The rate of change of velocity of an object with respect to time is known as acceleration.”
In terms of the formula:
Acceleration = \(\frac{\text { Change in Velocity }}{\text { Time Taken }}\)
\(\vec{a}=\frac{\Delta \vec{v}}{\Delta t}\)
The unit of acceleration in M.K.S. system is meter/second 2 (m/s2) Its dimensional formula is [M0L1F2]. Acceleration is a vector quantity. Similar to velocity it is also divided as follows:
Types of acceleration:
1. Average Acceleration: “The ratio of the total change in velocity to the total time taken is called average acceleration”.
If Δv is the change in velocity in it time interval, then;
Average acceleration (a) = \(\frac{\text { Total Change in Velocity }}{\text { Total Time Taken }}\)
= \(\left[\frac{\Delta v}{\Delta t}\right]\)
2. Instantaneous Acceleration:
Instantaneous acceleration is defined as “acceleration at any given point or at any instant of time.” If at Δt time interval velocity is Δv then according to the above definition; to calculate instantaneous acceleration
Δt → 0. Hence,
Here, \(\frac{d v}{d t}\), differentiation of v with respect to time t which can be known mathematically.
Here \(\frac{d^{2} x}{d t^{2}}\) double differentiation of x w.r.t. t which can he calculated mathematically.
Therefore, instantaneous acceleration is the differentiation of velocity with respect to time and is double differentiation of displacement w.r.t. time.
For any moving object at definite time intervals, if the change in velocity is also the same then this is known as uniform acceleration. And if the changes are different in velocity then this is non-uniform acceleration. In the same accelerated motion, average acceleration and instantaneous acceleration are the same.
If in any circular motion (path), the magnitude of the velocity of the moving object does not change but the direction of the moving object changes continuously, they this type of motion is also called accelerated motion.
Acceleration can be positive, negative or zero. If acceleration is positive its velocity increases. If acceleration is zero then the object moves with a constant speed (velocity). And if the acceleration is negative then the velocity of the object decreases. Hence, negative acceleration is called retardation.