Question

A skier has an deceleration of `2.5` `m``/``s^2`. How long does it take her to come to a complete stop from a speed of `18` `m``/``s`?

Answer 1

It takes her 7.2 seconds to come to a complete stop.

Explanation:

The skier is slowing from a speed of `18 " m/s"` to `0 " m/s",` at a rate of `–2.5 " m/s"^2.` Her speed is decreasing by `2.5 " m/s"` every second.

Think of it like this: she starts with `18` units of velocity, and every second, she loses `2.5` units of velocity.

At this rate, how many seconds will it take for her to lose all `18` units of velocity?

This we can write as an equation:

`[(2.5),("units/second")] xx [(t),("seconds")] = [(18),("units")]`

or simply

`2.5 t = 18`

Solving for `t`:

`(cancel2.5t)/cancel2.5=18/2.5`

`t = 7.2`

So it will take 7.2 seconds to lose all 18 units of velocity.

---

This process is more commonly represented in Physics by the following equation:

`v_f - v_i = at`

where

• `v_f` is the `f`inal `v`elocity,
• `v_i` is the `i`nitial `v`elocity,
• `a` is the `a`cceleration (negative when slowing down), and
• `t` is the `t`ime taken.

Using this equation (with units) on this problem gives

`0" m/s" - 18" m/s" = (–2.5 " m/s"^2)t`

`(–18" m/s")/(–2.5 " m/s"^2) = t`

`7.2" "cancel"(m/s)"/(cancel"(m/s)""/s") = t`

`7.2 " s" = t`

which is the same answer as before.