Question #2052e

1 Answer
Apr 6, 2016

If the girl is accelerating at 1.14 m/s^21.14ms2, it will take her about 7.29s7.29s to increase her speed by 8.32m/s8.32ms.

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*tvf=vi+at

2) v_f-v_i=a*tvfvi=at

3) (v_f-v_i)/a=tvfvia=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!