Name: ___________________
Date: _________________
Physics I H
Mr. Tiesler
Solutions to Representing Motion Homework Problems 6-10
6.) You are driving home from school steadily at 95 km h for 130 km. It then begins to rain and
you slow to 65 km h. You arrive home after driving 3 hours and 20 minutes. (a) How far is your
hometown from school? (b) What was your average speed?
The time for the first part of the trip is calculated from the initial speed and the first distance.
d1
ave speed1  v1 
 t1 
t1
d1
v1

130 km
95 km h
 1.37 h  82 min
The time for the second part of the trip is therefore
t2  ttot  t1  3.33 h  1.37 h  1.96 h  118 min
The distance for the second part of the trip is calculated from the average speed for that part of the
trip and the time for that part of the trip.
ave speed 2  v2 
d2
t2
 d 2  v2 t2   65 km h 1.96 h   127.5 km  1.3 10 2 km
2
(a) The total distance is then dtotal  d1  d 2  130 km  127.5 km  257.5 km  2.6 10 km
(b) The average speed is NOT the average of the two speeds. Use the definition of average
speed.
ave speed 
dtotal
ttotal

257.5 km
3.33 h
 77 km h
7.) A person jogs eight complete laps around a quarter-mile track in a total time of 12.5 min.
Calculate (a) the average speed and (b) the average velocity, in m s .
The distance traveled is 2.0 miles  8 laps  0.25 mi lap  . The displacement is 0 because the ending
point is the same as the starting point.
(a) Average speed =
d
t

2.0 mi
12.5 min
 2 mi   1610 m  1 min 

  4.3 m s

 12.5 min   1 mi  60 s 

(b) Average velocity = v  x t  0 m s
8.) An airplane travels 3100 km at a speed of 790 km h , and then encounters a tailwind that
boosts its speed to 990 km h for the next 2800 km. What was the total time for the trip? What was
the average speed of the plane for this trip?
The average speed for each segment of the trip is given by v 
For the first segment, t1 
d1
v1
For the second segment, t2 

d2
v2
3100 km
790 km h

d
t
, so t 
d
v
for each segment.
 3.924 h .
2800 km
 2.828 h .
990 km h
Thus the total time is ttot  t1  t2  3.924 h  2.828 h  6.752 h  6.8 h .
The average speed of the plane for the entire trip is
v 
d tot
t tot

3100 km  2800 km
 873.8  8.7  10 km h .
2
6.752 h
9.) A person travels by car from one city to another with different constant speeds between pairs
of cities. She drives for 30.0 min at 80.0 km/h, 12.0 min at 100.0 km/h, and 45.0 min at 40.0
km/h and spends 15.0 min eating lunch and buying gas. (a) Determine the average speed for the
entire trip. (b) Determine the distance between the initial and final cities along the route.
10.) The Olympic record for the marathon is 2 h, 9 min, 21 s. The marathon distance is 26 mi,
385 yd. Determine the average speed (in mi/h) of the record.