Question

While mentioning acceleration the time is mentioned two times. Why?

Answer 1

Hint: Before we get to the question, let's talk about the acceleration. In mechanics, acceleration is the rate at which an object's velocity changes with respect to time. The term "acceleration" refers to a quantity that is measured in vectors (in that they have magnitude and direction). The SI unit for acceleration is the metre per second squared $\left( {m \cdot {s^{ - 2}}} \right)$.

Complete step by step answer:
The rate of change of velocity with time is called acceleration, while the rate of change of displacement with time is called velocity. Because both words are time dependent, time is mentioned twice in the case of acceleration.

Explanation: The rate of change of velocity is referred to as acceleration.
$a = \dfrac{v}{t}$
The rate of change of displacement is called velocity.
$v = \dfrac{s}{t}$
As a result, acceleration can be expressed as,
$a = \dfrac{v}{t} \\
\Rightarrow a= \dfrac{{\dfrac{s}{t}}}{t} \\
\therefore a= \dfrac{s}{{{t^2}}}$
As a result, the unit of acceleration is \[m \cdot {s^2}\].

As a result, while describing acceleration, time is taken into account twice.

Note: It should be emphasised that it is impossible to tell whether an observable force is due to gravity or acceleration unless the object's state of motion is known; gravity and inertial acceleration have identical effects. The equivalence principle, coined by Albert Einstein, states that only observers who feel no force at all, including gravity, are justified in judging that they are not accelerating.