Question

You start out by driving 107 miles north in 2 hours and 20 minutes, and then you stop and park for a while. Finally you drive another 54 miles south in 2 hours and 6 minutes. The average velocity for your entire trip was 29.05 miles per hour to the south. How much time did you spend parked?

a) 2 hours 12 minutes

b) 0 hours 33 minutes

c) 5 hours 32 minutes

d) 1 hour 6 minutes

Answer 1

Solution:

Average velocity is given as V = 29.02 miles/hour to the south

Average velocity can be defined as the ratio of total displacement to total time taken.

Let the time taken to park the vechile is Tp.

therefore total time taken T = 2 hours 20 min + Tp + 2 hours 6 min

T = 4 hours + 26 min + Tp

T = 4 hours + 26/60 hour + Tp (since 1 hour = 3600 s and 1 min = 60 sec)

T = 4.4333 + Tp (hours)

And total displacement D = 107 miles - 54 miles

D = 53 miles

D = 53 x 1609.34 m (since 1 miles = 1609.34 m)

D = 85295.2 m

Now Average velocity V = D/T

29.02 = 53/(4.4333 + Tp)

T = - 2.6 hours (Time never be negative, but we can say it is wasted)

Therefore the nearest choice is option (A)