Question #e7978

The idea here is that the average acceleration of an object can be described as the average change in velocity, `Deltav`, that occurs in a given time interval, `Deltat`.

In other words, the average acceleration tells you the rate at which the velocity of the object changed from an initial value to a final value in a period of time.

`color(purple)(bar(ul(|color(white)(a/a)color(black)(a_"avg" = "change in velocity"/"change in time" = (Deltav)/(Deltat))color(white)(a/a)|)))`

The change in velocity can be calculated by subtracting the initial velocity from the final velocity

`Deltav = v_"final" - v_"initial"`

In this case, the treadmill started from rest, which means that `v_"initial" = 0`. You thus have

`Deltav = v_"final"`

The change in time is said to be equal to `5` minutes. In this case, it doesn't matter when the treadmill started moving, all that matters is the total time it spent moving. You thus have

`Deltat = "5 min"`

Now, notice that the average acceleration is given in meters per second per second, `"m/s/s"`, which is another way of expressing meters per square second, `"m/s"^2`.

Convert the change in time from minutes to seconds

`5 color(red)(cancel(color(black)("min"))) * "60 s"/(1color(red)(cancel(color(black)("min")))) = "300 s"`

You now have what you need to use the equation for average acceleration

`a_"avg" = v_"final"/(Deltat)`

Rearrange to solve for `v_"final"`

`v_"final" = a_"avg" * Deltat`

Plug in your values to find

`v_"final" = 4.7 * 10^(-3)"m"/("s" * color(red)(cancel(color(black)("s")))) * 300color(red)(cancel(color(black)("s")))= color(green)(bar(ul(|color(white)(a/a)color(black)("1.4 m/s")color(white)(a/a)|)))`

I'll leave the answer rounded to two sig figs, but keep in mind that you only provided one sig fig for the time interval.