Your friend left your house and is now driving 40 miles per hour, but she has been speeding up the whole time since she left your house, and has gone 10 miles. How long has she been driving?

Question

Quizplus · Accepted Answer

We can use the formula for uniform acceleration, Vf = Vi + at, where Vf is final velocity, Vi is initial velocity, a is acceleration, and t is time. In this case, we know that Vi = 0 (since she started from rest), Vf = 40 mph, and a = unknown. We can rearrange the formula to solve for a:

a = (Vf - Vi)/t = Vf/t

So, acceleration is simply equal to final velocity divided by time. We also know that she has covered a distance of 10 miles, which we can convert to feet (since acceleration is usually given in units of feet per second squared):

10 miles * 5280 feet/mile = 52,800 feet

We can use the formula for distance with uniform acceleration, d = Vi*t + 1/2*a*t^2, where d is distance and all other variables are as defined above. We can rearrange the formula to solve for time:

t = sqrt(2d/a)

Plugging in the values we know, we get:

t = sqrt(2*52,800/Vf)

t = sqrt(2*52,800/40)

t ≈ 26.4 minutes

Since the question asks how long she has been driving and not how long it will take her to reach her destination, the answer is B, longer than 15 minutes.

Your Friend Left Your House and Is Now Driving 40