Question

Question #3b237

Answer 1

`v_f = 22 " 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 `Deltax` it travels. Our goal is to find the final velocity `v_f` of the car.

Which UAM formula uses `v_i`, `v_f`, `Deltax`, and `t`?

`Deltax = ((v_i+v_f)/2)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:

`Deltax = ((v_i+v_f)/2)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 `"km"` to `"m"`, and `"min"` to `"s"`.

`3.6 " km" * (1000 " m")/"km" = 3600 " m"`

`4.4 " 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 " 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 " m/s"`

Final Answer