Question
Define the instantaneous velocity and instantaneous acceleration and explain the difference.
✓
Answer
Instantaneous velocity and instantaneous acceleration :
Instantanous velocity : The velocity of an object at a definite instance is called instantaneous velocity.
Vector form $\quad \vec{v}=\frac{\overrightarrow{d x}}{d t}$
when the value of $\Delta t$ decreases to zero.
Thus instantaneous acceleration
Vector form $\vec{a}=\frac{d \vec{v}}{d t}$
Difference between instantaneous velocity and instantaneous acceleration :
Instantanous velocity : The velocity of an object at a definite instance is called instantaneous velocity.
Vector form $\quad \vec{v}=\frac{\overrightarrow{d x}}{d t}$
when the value of $\Delta t$ decreases to zero.
Thus instantaneous acceleration
Vector form $\vec{a}=\frac{d \vec{v}}{d t}$
Difference between instantaneous velocity and instantaneous acceleration :
| Instantaneous velocity | Instantaneous acceleration |
| (i) Its unit is $m / s$ and dimension is $M ^0 L^1 T^{-1}$. | (i) Its unit is $m / s ^2$ and dimension is $M ^0 L^1 T^{-2}$ |
| (ii) Its value is equal to the first differential with respect to time of displacement. | (ii) Its value is equal to the second derivatives of displacement with respect to time. |
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