Question #2052e

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Question #2052e

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Answer 1 · 2016-04-06T01:41:34

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

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) $v_{f} = v_{i} + a \cdot t$ $v_f=v_i+a*t$

2) $v_{f} - v_{i} = a \cdot t$ $v_f-v_i=a*t$

3) $\frac{v_{f} - v_{i}}{a} = t$ $(v_f-v_i)/a=t$

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 $8.32$ !

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Question #2052e

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