Question

Question #117eb

Answer 1

`"change in velocity" = -20hati - 20hatj`

(taking positive `x`-direction is east and positive `y`-direction is north)

Explanation:

Velocity is a vector quantity that describes both the magnitude and direction of the change in position of an object.

Since the speed is constant the only part of the velocity that changes is the direction.

We can calculate this change in velocity via components, taking the positive `x`-axis to be east and the positive `y`-axis to be north.

When the truck was traveling north at a rate of `20` `"m/s"`, we describe the velocity in unit vector components as

`vecv_1 = overbrace(0hati)^(x"- component") + overbrace(20hatj)^(y"- component")`

During the second part, when it was traveling west (also at `20` `"m/s"`), we have

`vecv_2 = -20hati + 0hatj`

We can describe the change in velocity as the final value minus the initial value:

`color(blue)(Deltavecv) = vecv_2 - vecv_1 = (-20hati + 0hatj) - (0hati + 20hatj) = color(blue)(ulbar(|stackrel(" ")(" "-20hati - 20hatj" ")|)`

That is to say, the net change in horizontal velocity went down by magnitude `20` (i.e. from `0` to `-20`), and the net change in vertical velocity went down by magnitude `20` (i.e. from `20` to `0`).