Question

The position of a particle moving along a straight line, in meters, is given by s= 6/t, where t represents time, in seconds. Calculate the average velocity of the particle, in meters per second, on the time interval [1,3]

Answer 1

The average velocity of the particle on the time interval is -2 meters per second.

Explanation:

Let be
`s(t)` the position curve which is continuous on the time interval
`[a,b]`. The average velocity (
`\bar v`), measured in meters per second, on the time interval is represented by the following expression:

`\bar v = (s(b) -s(a))/(b-a)`

Where:

`a`,
`b` - Initial and final times, measured in seconds.

`s(a)`,
`s(b)` - Initial and final positions, measured in meters.

If we know that
`s(t) = (6)/(t)`,
`a = 1\,s` and
`b = 3\,s`, the average velocity of the particle on the time interval is:

`s(a) = 6\,(m)/(s)`

`s(b) = 2\,(m)/(s)`

`\bar v = (2\,(m)/(s)-6\,(m)/(s) )/(3\,s-1\,s)`

`\bar v = -2\,(m)/(s)`

The average velocity of the particle on the time interval is -2 meters per second.