Be the first to answer - "How acceleration is equal to d 2 x..."

High School
Physics
Force, Motion and Energy
Acceleration Due to Gravity

podtarta7hx

Answered question

2022-12-08

How acceleration is equal to

d^{2} x / d t^{2}

Answer & Explanation

Bearzlvq

Beginner2022-12-09Added 1 answers

the definition of a derivative is the change in one variable with respect to another. For instance, the change in position with respect to time is what is meant by velocity. You could do this experiment and calculate velocity as:

V = (x_{2} - x_{1}) / (t_{2} - t_{1})

now imagine that we start shrinking the distance between our measurements until the distance between them is infinitesimally small. This is shown using the 'd' notation. So Velocity becomes:
V = dx/dt
where dx = change in position
and dt = change in time
Acceleration is the change in velocity with respect to time or:
a = dV/dt
but V = dx/dt
dx/dt is called a first derivative, so taking the derivative of this quantity with respect to t again gives us the second derivative,

d^{2} x / d t^{2},

or in words... the change in the change in position with respect to time.

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