NEET Foundation Notes For Physics Chapter 1 Motion Rate of Change of Velocity
Acceleration
In our daily life, the velocity of a moving object tends to vary a lot either in magnitude or in direction. We express this change in another physical quantity called acceleration. Acceleration is the rate of change of velocity with time, i.e., change in velocity per unit time. Numerically, it is expressed as:
\(\text { Acceleration }=\frac{\text { change in velocity }}{\text { time interval }}=v-\frac{u}{t}\)For example, the direction of acceleration is along the direction of change in velocity of the body. Acceleration is vector quantity which can be negative, positive or zero depending on the change in the velocity. The direction of acceleration is along the direction of changes in velocity of the body.
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Retardation
Negative acceleration or retardation is the decrease in velocity per second. For retardation, the direction of the velocity is opposite to the direction of the acceleration.
Let us understand these with the following example.
Example
Let an object move in a straight line in the same direction with an initial velocity of u. After some time t, its velocity u becomes v.
So, change in velocity = v – u
Time interval = t
\(\text { Acceleration }=\frac{\text { change in velocity }}{\text { time interval }}\)Therefore, Acceleration a = \(\frac{v-u}{t}\)
a t = v – u
v = u + a t
a = acceleration, if v > u, a is positive
a = retardation, if v < u, a is negative
Unit
\(\text { Unit of acceleration }=\frac{\text { Unit of velocity }}{\text { Unit of time }}\)SI unit of acceleration = \(\frac{\mathrm{m} / \mathrm{s}}{\mathrm{s}}=\mathrm{ms}^{-2}\)
CGS. unit of acceleration = cm-2
Uniform Acceleration
The uniform acceleration is one when equal changes in velocity take place in equal intervals of time.
Example: Free fall of a ball, which shows the motion of a body under gravity.
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Variable Acceleration
If change in velocity is not same in the same intervals of time, it is called variable acceleration. For example, car moving in a crowded market.
Whenever the magnitude of velocity decreases, the rate of change of velocity is referred as retardation or deceleration. It is not necessary that the rate of change of velocity, i.e., the acceleration is always constant. In situation where the rate of change of velocity of a body in motion is not constant, the body is said to be moving with non-uniform acceleration or variable acceleration.
Acceleration due to Gravity
When an object falls freely, the acceleration produced in the body due to earth’s gravitational attraction is called acceleration due to gravity. It is donated by the letter g.
g = 9.8 m/s2 (downward)
(~ 10 m/s2, downward)
Due to gravitational force, all objects are accelerated towards the earth. This uniform acceleration towards the earth, irrespective of the mass is known as acceleration due to gravity and is denoted by ‘g’.
Equations of Uniform Accelerated Motion
Relation among velocity, distance, time, and acceleration is called equations of motion. There are three equation of motion for bodies moving with uniform acceleration.
First Equation of Motion:
v = u + at (1)
Second Equation of Motion:
s = \(u t+\frac{1}{2} a t^2\) (2)
Third Equation of Motion:
v2 = u2 + 2as (3)
Here,
v = final velocity of body
u = initial velocity of body
a = acceleration
t = time take by body
s = distance travelled by body in time t.
Average Velocity in Uniform Acceleration Motion
If a body move ‘s’ distance in ‘t’ time interval. Then,
\(\text { Average velocity }=\frac{\text { displacement }}{\text { time }}\)=\(\frac{s}{t}\)
= \(\frac{u t+\frac{1}{2} a t^2}{t}\)
= \(u t+\frac{1}{2} a t\)
= \(u t+\frac{1}{2}(v-u)\)
= \(u+\frac{v}{2}-\frac{u}{2}\)
= \(\frac{u}{2}+\frac{v}{2}=\frac{u+v}{2}\)
Here ‘a’ is uniform acceleration of body.