Question

Question #a4a88

Answer 1

`4.44444... or 40/9` seconds if it is asking for time taken.

Explanation:

I will being using 'uvast' eqautions to solve this, I suggest you look that up online (Also commonly called SUVAT) if you are not familiar with it.

we know that `a` (acceleration) `= 5 m s ^-2` or 5 metres per second squared

we know that `u` (initial velocity) `= 0ms^-1` or 0 metres per second because the car starts 'from rest'

we know that `v` (final velocity) `= 80`km/h or 80 kilometres per hour.

Firstly, all values should be in the standard units (metres, seconds, etc.) so we have to convert `v` into metres per second.

80km/h = `80 times 1000m` per `60 times 60s`

A kilometre is 1000m long and there is 80 of them.
An hour has 60 minutes, each minute containing 60 seconds.

Therefore `80` km/h = `80,000`m/ `3600`s

We want it in the format metres per 1 second, so we must divide both sides by 3600 to get this 1 second.

`80`km/h = `80,000`m / `3600`s `->` `80000/3600`m/s

If you put `80000/3600` into your calculator you get 22.222222....

I recommend not changing it to a decimal and instead just simplifying it to `200/9`m/s

Now we know that `v` = `200/9ms^-1` (the same as m/s)

It is hard to tell if the question is looking for the distance that the car will have traveled or the time that it will have taken because it just says "how long will it have traveled by the time.."

If you want the time taken, you want to find the value for `t`

using the equation `v = u +at`, rearrange to give `t = (v-u)/a`

fill in our known values and get `t = (200/9 - 0)/5`

`t=4.444... or 40/9` seconds

if you want the distance traveled you are looking for `s` (this actually represents displacement, but don't get caught up with that for now) and you use the equation `s = ut + 1/2 at^2` however I don't think the question is looking for that.