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Motion in a Plane — Physics STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 SciencePhysicsMotion in a Plane4 Marks
Question
Explain the terms:
  1. Acceleration
  2. Average acceleration
  3. Instantaneous acceleration
✓

Answer

1. Acceleration:
• Acceleration is the rate of change of velocity with respect to time.
• It is a vector quantity.
• Dimension: $\left[ M ^0 L^1 T^{-2}\right]$
• If a particle moves with constant velocity, its acceleration is zero.
2. Average acceleration:
• Average acceleration is the change in velocity divided by the total time required for the change.
• If $\overrightarrow{ v _1}$ and $\overrightarrow{ v _2}$ are the velocities of the $T$ particle at time $t_1$ and $t_2$ respectively, then the change in velocity is and time required for this change is $\Delta t=t_2-t_1$
$\therefore \vec{a}_{a v}=\frac{\vec{v}_2-\vec{v}_1}{t_2-t_1}=\frac{\Delta \vec{v}}{\Delta t}$
3. Instantaneous acceleration:
• The instantaneous acceleration a is the limiting value of the average acceleration of the object over a small time interval ' $\Delta t$ ' around $t$ when the value of time interval goes to zero.
$\overrightarrow{ a }_{\text {inst }}=\lim _{\Delta t \rightarrow 0} \frac{\Delta \overrightarrow{ v }}{\Delta t }=\frac{ d \overrightarrow{ v }}{ dt }$
• Instantaneous acceleration is the slope of the tangent to the velocity-time graph at a position corresponding to given instant of time.
[Note: Generally, when the term acceleration is used, it is an instantaneous acceleration.]

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