Question

Question #2052e

Answer 1

If the girl is accelerating at `1.14 m/s^2`, it will take her about `7.29s` to increase her speed by `8.32m/s`.

Explanation:

First we’ll show the math, a derivation of the solution (in 6 steps). Then, we’ll explain each step in more detail.

1) `v_f=v_i+a*t`

2) `v_f-v_i=a*t`

3) `(v_f-v_i)/a=t`

4) `(Deltav)/a=t`

5) `(8.32m/s)/(1.14 m/s^2)=t`

6) `t=7.29s` ...and we're Done!!!!

1) Why did we choose this formula? Well, the second sentence asks a question containing the key phrase "increase ....speed". Ask yourself, what equations involve changing speed (due to a force or acceleration). There are two

`v_f=v_i+a*t`

and

`v_f^2=v_i^2+2*a*d`

The 1st equation describes the change in speed when an object (or girl in this case) experiences an acceleration, `a`, for a length of time, `t`.

The 2nd equation describes the change in speed when an object experiences an acceleration, `a`, as it travels over a distance, `d`.

We chose the first equation here because the phrase "how long" refers to length of time!

What do the physical quantities (variables) in the equation we've chosen represent?

`v_i` is initial speed (or velocity)
`v_f` is final speed (or velocity)
`a` is acceleration (the rate at which an object changes speed)
`t` the amount of time the object experiences acceleration

2) In the 2nd step, we're just subtracting `v_i` from both sides

3) Here, we're just dividing both sides by `a`

4) Uh oh! we don't know the initial and velocities `v_i` and `v_f`! But that's ok! We only need to know the "increase in her speed", which is the DIFFERENCE between them for this problem. We denote this difference as `Deltav` (pronounced "delta v" or the "change in `v`"). In other words, `Deltav=v_f - v_i`.

5) They tell us in the problem that the girl's acceleration `a=1.14m/s^2` and her increase in speed `Deltav=8.32m/s`. So we replace the variables with their corresponding values.

6) The last step is arithmetic. We just divide to find `t`! So `t` is how long it takes her to increase her speed by `8.32`!