# The distance, s, of a moving body from a fixed point is given as a function of time, t, by s = 20...

## Question:

The distance, s, of a moving body from a fixed point is given as a function of time, t, by {eq}\displaystyle s = 20 e^{\dfrac t2} {/eq}. Find the velocity, v, of the body as a function of t.

## Velocity

The velocity of an object is defined as the rate at which the object is traveling. More velocity means the object is moving faster and less velocity means object is moving slower. The velocity is a vector quantity and the SI unit of velocity is m/s. Mathematically velocity is given by

{eq}\begin{align} v = \frac{ds}{dt} \end{align} {/eq}

## Answer and Explanation:

**Data Given**

- The position of the moving body is given by {eq}s = 20 e^{\frac{t}{2}} {/eq}

We know that velocity is given by

{eq}\begin{align} v = \frac{ds}{dt} \\ v = \frac{d \left ( 20 e^{\frac{t}{2}} \right )}{dt} \\ v = 20 e^{\frac{t}{2}} \times \frac{1}{2} \\ \color{blue}{\boxed{ \ v = 10 e^{\frac{t}{2}} \ }} \end{align} {/eq}

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