# Question 3b237

Oct 12, 2017

${v}_{f} = 22 \text{ m/s}$

#### Explanation:

This problem gives us the initial velocity ${v}_{i}$ of the car, the time $t$ in which it accelerates, and the distance $\Delta x$ it travels. Our goal is to find the final velocity ${v}_{f}$ of the car.

Which UAM formula uses ${v}_{i}$, ${v}_{f}$, $\Delta x$, and $t$?

$\Delta x = \left(\frac{{v}_{i} + {v}_{f}}{2}\right) t$

This equation is perfect -- it gives us a way to plug in everything we know and only have our one variable ${v}_{f}$ left to solve for! So, let's do just that:

$\Delta x = \left(\frac{{v}_{i} + {v}_{f}}{2}\right) t$

3.6 " km" = ((5.3" m/s" + v_f)/2)(4.4 " min")

Before we continue to solve this, you may notice a few units that are out of place. We should convert $\text{km}$ to $\text{m}$, and $\text{min}$ to $\text{s}$.

$3.6 \text{ km" * (1000 " m")/"km" = 3600 " m}$

$4.4 \text{ min" * (60 " s")/"min" = 264 " s}$

Now that we have our converted values, we can continue to solve the equation.

3600 " m" = ((5.3" m/s" + v_f)/2)(264 " s")

3600 " m" = (5.3" m/s" + v_f)(132 " s")

3600 " m" = 699.6 " m" + (132" s")(v_f)

2900.4 " m" = (132 " s")(v_f)#

$21.97 \text{ m/s} = {v}_{f}$

This is the final velocity of the car after the 4.4 minutes. However, since the problem only gave us an accuracy of 2 significant figures, our answer should also only have 2 significant figures.

${v}_{f} = 22 \text{ m/s}$