Question

A fox starts from rest and accelerates at `1.1` `"m"*"s"^(-2)"`. How long does it take the fox to cover `5.0` `"m"`?

Answer 1

You will need one of the kinematics equations to solve this problem.

The solution is that it will take the fox `3.0` `s` to travel `5` `m`.

Explanation:

Here are your known variables;

`u = 0` `ms^-1` (It starts from rest)

`a = 1.1` `ms^-2`

`s = 5` `m`

The suitable equation would be:

`s = ut + 1/2at^2`

`5 = 0t+ 1/2(1.1)t^2`

The first term goes to `0`, so we have:

`5 = 1/2(1.1)t^2`

Rearranging to make `t` the subject:

`t = sqrt((2xx5)/1.1) = sqrt (10/1.1) = sqrt 9.09`

Final answer: 3.0 seconds

Answer 2

It will take the fox `"3 s"` to run `"5m"` starting from rest and accelerating at `"1.1 m/s"^2"`.

Explanation:

This is a kinematics question . You have initial velocity, `v_i`, displacement, `Deltad`, and acceleration, `a`. You want to find `Deltat`. With these variables, you would use the following kinematic equation:

`Deltad=v_it+1/2aDeltat^2`

Since `v_i=0`, you can rewrite the equation as:

`Deltad=1/2aDeltat^2`

Organize your data:

Known

`v_i=0`

`a="1.1 m/s^2"`

`Deltad="5 m"`

Unknown

`Deltat`

Solution

Rearrange the equation to isolate `Deltat` on the left. Insert the data and solve.

`Deltat^2=(2d)/a`

`Deltat^2=(2xx5color(red)cancel(color(black)("m")))/(1.1color(red)cancel(color(black)("m"))/"s"^2)="9 s"^2"` rounded to one sig fig

`Deltat=sqrt(9"s"^2)="3 s"`