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Acceleration - (Concept)

  1. Definition: Rate of change of velocity with time.

    $$
    \vec{a}=\frac{\text { change in velocity }}{\text { time taken }}=\frac{\vec{v}_f-\vec{v}_i}{t}
    $$

    - Tips for Acceleration-
    1. The body is said to have undergone acceleration if there is a change in velocity i.e., :
    - Change in speed
    - Change in direction
    - Change in both
    2. It is a vector quantity
    3. Dimension $=L T^{-2}$
    4. S.I unit $=m \mathrm{~s}^{-2}$

    Example: A car starting from rest accelerates uniformly to a speed of $75 \mathrm{~m} / \mathrm{s}$ in 12 seconds. What is the car's acceleration?
    Solution: $v_i=0$ (starting from rest)

    $$
    v_f=75 \mathrm{~m} / \mathrm{s}
    $$


    From the definition of acceleration we know that,

    $$
    \begin{aligned}
    a & =\frac{v_f-v_i}{t} \\
    & =\frac{75-0}{12}
    \end{aligned}
    $$
     

                                           

    $$
    \mathrm{a}=6.25 \mathrm{~m} / \mathrm{s}^2
    $$


    There are four types of acceleration
    - Average acceleration- Total change in velocity per unit time taken is the average acceleration

    $$
    \text { Avg. acceleration }\left(\vec{a}_{a v g}\right)=\frac{\Delta \vec{v}}{\Delta t}
    $$

    - Instantaneous acceleration - Infinitesimal change in velocity per unit time taken is the average acceleration

    $$
    \text { Inst. acceleration }\left(\vec{a}_{\text {inst }}\right)=\frac{d \vec{v}}{d t}
    $$
     

  2. Uniform acceleration- Change in velocity per unit time is constant.
  3. Non-uniform acceleration- Change in velocity per unit time is not constant. If the velocity and acceleration are directed in the opposite direction
  • Slowing down or deceleration  If the change in velocity is directed towards a negative direction (right to left) then acceleration is positive.
  • Speeding up or acceleration If the change in velocity is directed towards a positive direction (left to right) then acceleration is positive.
  • Negative Acceleration- Important terms related to acceleration.
Exam Chapter
JEE MAIN Kinematics
Physics Part I Textbook for Class XI
Page No. : 45
Line : 48

Acceleration is the rate of change of velocity with time.

The average acceleration \bar{a} over a time interval is defined as the change of velocity divided by the time interval :

\bar{a} = \frac{v_{2}-v_{1}}{t_{2}-t_{1}}= \frac{\Delta v}{\Delta t}


Concepts of Physics Part-1
Page No. : 34
Line : 57

Understanding Physics (Volume-1)
Page No. : 132
Line : 3

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