Question #2052e

1 Answer
Apr 6, 2016

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#!