Question

the velocity of a particle any time t is given by v=|t-2| m/s. The average velocity between t=0 to t=3 second is

Answer 1

The answer is, $-\frac{1}{2} \frac{m}{s}$

Functional integration is a collection of results in mathematics and physics where the domain of an integral is no longer a region of space, but a space of functions.

Integration is the algebraic method to find the integral for a function at any point on the graph.

Finding the integral of some function with respect to some variable x means finding the area to the x-axis from the curve.

What is the difference between integration and differentiation?

Differentiation is used to study the small change of a quantity with respect to unit change of another. (Check the Differentiation Rules here).

On the other hand, integration is used to add small and discrete data, which cannot be added singularly and represented in a single value.

According to the question:

Given function $=V=|t-2|m|s$,

$=\int\limits^3_0 {v} \, dt$

$=\int\limits^3_0 (t-2) \, dx =|\frac{t^2}{2\times 3}-\frac{2t}{3} |^3_0=|\frac{3\times \gamma^2}{2\times 8}-\frac{2\times 8}{8} |$

$=\frac{3-4}{2}=-\frac{1}{2}m/s$

Hence, the average velocity between t=0 to t=3 second is, $-\frac{1}{2} \frac{m}{s}$.

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