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"?

Jun 3, 2017

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:

$u = 0$ $m {s}^{-} 1$ (It starts from rest)

$a = 1.1$ $m {s}^{-} 2$

$s = 5$ $m$

The suitable equation would be:

$s = u t + \frac{1}{2} a {t}^{2}$

$5 = 0 t + \frac{1}{2} \left(1.1\right) {t}^{2}$

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

$5 = \frac{1}{2} \left(1.1\right) {t}^{2}$

Rearranging to make $t$ the subject:

$t = \sqrt{\frac{2 \times 5}{1.1}} = \sqrt{\frac{10}{1.1}} = \sqrt{9.09}$

Jun 3, 2017

It will take the fox $\text{3 s}$ to run $\text{5m}$ starting from rest and accelerating at $\text{1.1 m/s"^2}$.

Explanation:

This is a kinematics question . You have initial velocity, ${v}_{i}$, displacement, $\Delta d$, and acceleration, $a$. You want to find $\Delta t$. With these variables, you would use the following kinematic equation:

$\Delta d = {v}_{i} t + \frac{1}{2} a \Delta {t}^{2}$

Since ${v}_{i} = 0$, you can rewrite the equation as:

$\Delta d = \frac{1}{2} a \Delta {t}^{2}$

Known

${v}_{i} = 0$

$a = \text{1.1 m/s^2}$

$\Delta d = \text{5 m}$

Unknown

$\Delta t$

Solution

Rearrange the equation to isolate $\Delta t$ on the left. Insert the data and solve.

$\Delta {t}^{2} = \frac{2 d}{a}$

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"