chapter 16 speed and velocity AWS
CHAPTER 16 SPEED AND VELOCITY EXERCISE 65, Page 162
1. A train covers a distance of 96 km in 1 h 20 min. Determine the average speed of the train (a) in km/h and (b) in m/s
(a) Average speed =
(b) 72 km/h =
dis tan ce travelled 96 km 96 km/h = 72 km/h 20 time taken 1 h 1.3 60
72 km / h 1000 m / km 72 m / s = 20 m/s 60 60s / h 3.6
2. A horse trots at an average speed of 12 km/h for 18 minutes; determine the distance covered by the horse in this time
Average speed =
dis tan ce travelled time taken
from which, distance covered = speed × time taken = 12 km/h × 18/60 h = 3.6 km
3. A ship covers a distance of 1365 km at an average speed of 15 km/h. How long does it take to cover this distance ?
Average speed =
dis tan ce travelled time taken
from which, time taken =
=
dis tan ce travelled average speed
91 1365 km = 91 hours = days = 3 days 19 hours 24 15 km / h
218 © John Bird Published by Taylor and Francis
EXERCISE 66, Page 164
1. Using the information given in the distance/time graph shown below, determine the average speed when travelling from 0 to A, A to B, B to C, 0 to C and A to C
Average speed from 0 to A =
dis tan ce travelled 30 km = 30 km/h time taken 1.0 h
Average speed from A to B =
dis tan ce travelled (50 30) km 20 km = 40 km/h time taken (1.5 1.0) h 0.5 h
Average speed from B to C =
dis tan ce travelled (60 50) km 10 km = 10 km/h time taken (2.5 1.5) h 1h
Average speed from 0 to C =
dis tan ce travelled 60 km = 24 km/h time taken 2.5 h
Average speed from A to C =
dis tan ce travelled (60 30) km 30 km = 20 km/h time taken (2.5 1.0) h 1.5 h
2. The distances travelled by an object from point 0 and the corresponding times taken to reach A, B, C and D, respectively, from the start are as shown: Points
Start
A
B
C
D
Distance (m)
0
20
40
60
80
Time (s)
0
5
12
18
25
Draw the distance/time graph and hence determine the average speeds from 0 to A, A to B, B to C, C to D and 0 to D 219 © John Bird Published by Taylor and Francis
The distance /time graph is shown below.
Average speed from 0 to A =
dis tan ce travelled 20 m = 4 m/s time taken 5s
Average speed from A to B =
dis tan ce travelled (40 20) m 20 m = 2.86 m/s time taken (12 5) s 7s
Average speed from B to C =
dis tan ce travelled (60 40) m 20 m = 3.33 m/s time taken (18 12) s 6s
Average speed from C to D =
dis tan ce travelled (80 60) m 20 m = 2.86 m/s time taken (25 18) s 7s
Average speed from 0 to D =
dis tan ce travelled 80 m = 3.2 m/s time taken 25s
3. A train leaves station A and travels via stations B and C to station D. The times the train passes the various stations are as shown: Station
A
B
Times
10.55 am
11.40 am
C 12.15 pm
D 12.50 pm
The average speeds are: A to B, 56 km/h, B to C, 72 km/h, and C to D, 60 km/h Calculate the total distance from A to D. 220 © John Bird Published by Taylor and Francis
Average speed =
dis tan ce travelled time taken
from which, distance = speed × time
Distance from A to B = 56
km 45 h = 42 km h 60
Distance from B to C = 72
km 35 h = 42 km h 60
Distance from C to D = 60
km 35 h = 35 km h 60
Hence, distance from A to D = 42 + 42 + 35 = 119 km
4. A gun is fired 5 km north of an observer and the sound takes 15 s to reach him. Determine the average velocity of sound waves in air at this place.
Average velocity =
dis tan ce travelled time taken
1200 5 km = 1200 km/h or = 333.33 m/s 15 3.6 h 60 60
5. The light from a star takes 2.5 years to reach an observer. If the velocity of light is 330 10 6 m/s, determine the distance of the star from the observer in kilometres, based on a 365 day year
Average speed =
dis tan ce travelled time taken
from which, distance = speed × time
Hence, distance to the star = 330 106 m / s 2.5 365 24 60 60s = 2.6 1016 m or 2.6 1013 km
221 © John Bird Published by Taylor and Francis
EXERCISE 67, Page 165
1. The speed/time graph for a car journey is shown below. Determine the distance travelled by the car
Distance travelled = area under the speed/time graph. In the speed/time graph shown below, distance travelled = area A + area B + area C + area D + area E 1 5 10 1 10 10 1 10 = 20 20 10 30 30 2 60 60 2 60 60 2 60
=
5 1 5 3 5 2.5 = 12.5 km 6 3 6
2. The motion of an object is as follows: A to B, distance 122 m, time 64 s, B to C, distance 80 m at an average speed of 20 m/s, C to D, time 7 s at an average speed of 14 m/s 222 © John Bird Published by Taylor and Francis
Determine the overall average speed of the object when travelling from A to D
Distance
Time
A to B,
122 m
64 s
B to C,
80 m
80 =4s 20
C to D,
7 × 14 m = 98 m
7s
Totals:
300 m
75 s
Hence, the overall average speed of the object when travelling from A to D =
di tan ce 300 = 4 m/s time 75
EXERCISE 68, Page 166 Answers found from within the text of the chapter, pages 161 to 166.
EXERCISE 69, Page 167 1. (c) 2. (g) 3. (d) 4. (c) 5. (e) 6. (b) 7. (a) 8. (b) 9. (d) 10. (a) 11. (a) 12. (b) 13. (c) 14. (d)
223 © John Bird Published by Taylor and Francis
1. A train covers a distance of 96 km in 1 h 20 min. Determine the average speed of the train (a) in km/h and (b) in m/s
(a) Average speed =
(b) 72 km/h =
dis tan ce travelled 96 km 96 km/h = 72 km/h 20 time taken 1 h 1.3 60
72 km / h 1000 m / km 72 m / s = 20 m/s 60 60s / h 3.6
2. A horse trots at an average speed of 12 km/h for 18 minutes; determine the distance covered by the horse in this time
Average speed =
dis tan ce travelled time taken
from which, distance covered = speed × time taken = 12 km/h × 18/60 h = 3.6 km
3. A ship covers a distance of 1365 km at an average speed of 15 km/h. How long does it take to cover this distance ?
Average speed =
dis tan ce travelled time taken
from which, time taken =
=
dis tan ce travelled average speed
91 1365 km = 91 hours = days = 3 days 19 hours 24 15 km / h
218 © John Bird Published by Taylor and Francis
EXERCISE 66, Page 164
1. Using the information given in the distance/time graph shown below, determine the average speed when travelling from 0 to A, A to B, B to C, 0 to C and A to C
Average speed from 0 to A =
dis tan ce travelled 30 km = 30 km/h time taken 1.0 h
Average speed from A to B =
dis tan ce travelled (50 30) km 20 km = 40 km/h time taken (1.5 1.0) h 0.5 h
Average speed from B to C =
dis tan ce travelled (60 50) km 10 km = 10 km/h time taken (2.5 1.5) h 1h
Average speed from 0 to C =
dis tan ce travelled 60 km = 24 km/h time taken 2.5 h
Average speed from A to C =
dis tan ce travelled (60 30) km 30 km = 20 km/h time taken (2.5 1.0) h 1.5 h
2. The distances travelled by an object from point 0 and the corresponding times taken to reach A, B, C and D, respectively, from the start are as shown: Points
Start
A
B
C
D
Distance (m)
0
20
40
60
80
Time (s)
0
5
12
18
25
Draw the distance/time graph and hence determine the average speeds from 0 to A, A to B, B to C, C to D and 0 to D 219 © John Bird Published by Taylor and Francis
The distance /time graph is shown below.
Average speed from 0 to A =
dis tan ce travelled 20 m = 4 m/s time taken 5s
Average speed from A to B =
dis tan ce travelled (40 20) m 20 m = 2.86 m/s time taken (12 5) s 7s
Average speed from B to C =
dis tan ce travelled (60 40) m 20 m = 3.33 m/s time taken (18 12) s 6s
Average speed from C to D =
dis tan ce travelled (80 60) m 20 m = 2.86 m/s time taken (25 18) s 7s
Average speed from 0 to D =
dis tan ce travelled 80 m = 3.2 m/s time taken 25s
3. A train leaves station A and travels via stations B and C to station D. The times the train passes the various stations are as shown: Station
A
B
Times
10.55 am
11.40 am
C 12.15 pm
D 12.50 pm
The average speeds are: A to B, 56 km/h, B to C, 72 km/h, and C to D, 60 km/h Calculate the total distance from A to D. 220 © John Bird Published by Taylor and Francis
Average speed =
dis tan ce travelled time taken
from which, distance = speed × time
Distance from A to B = 56
km 45 h = 42 km h 60
Distance from B to C = 72
km 35 h = 42 km h 60
Distance from C to D = 60
km 35 h = 35 km h 60
Hence, distance from A to D = 42 + 42 + 35 = 119 km
4. A gun is fired 5 km north of an observer and the sound takes 15 s to reach him. Determine the average velocity of sound waves in air at this place.
Average velocity =
dis tan ce travelled time taken
1200 5 km = 1200 km/h or = 333.33 m/s 15 3.6 h 60 60
5. The light from a star takes 2.5 years to reach an observer. If the velocity of light is 330 10 6 m/s, determine the distance of the star from the observer in kilometres, based on a 365 day year
Average speed =
dis tan ce travelled time taken
from which, distance = speed × time
Hence, distance to the star = 330 106 m / s 2.5 365 24 60 60s = 2.6 1016 m or 2.6 1013 km
221 © John Bird Published by Taylor and Francis
EXERCISE 67, Page 165
1. The speed/time graph for a car journey is shown below. Determine the distance travelled by the car
Distance travelled = area under the speed/time graph. In the speed/time graph shown below, distance travelled = area A + area B + area C + area D + area E 1 5 10 1 10 10 1 10 = 20 20 10 30 30 2 60 60 2 60 60 2 60
=
5 1 5 3 5 2.5 = 12.5 km 6 3 6
2. The motion of an object is as follows: A to B, distance 122 m, time 64 s, B to C, distance 80 m at an average speed of 20 m/s, C to D, time 7 s at an average speed of 14 m/s 222 © John Bird Published by Taylor and Francis
Determine the overall average speed of the object when travelling from A to D
Distance
Time
A to B,
122 m
64 s
B to C,
80 m
80 =4s 20
C to D,
7 × 14 m = 98 m
7s
Totals:
300 m
75 s
Hence, the overall average speed of the object when travelling from A to D =
di tan ce 300 = 4 m/s time 75
EXERCISE 68, Page 166 Answers found from within the text of the chapter, pages 161 to 166.
EXERCISE 69, Page 167 1. (c) 2. (g) 3. (d) 4. (c) 5. (e) 6. (b) 7. (a) 8. (b) 9. (d) 10. (a) 11. (a) 12. (b) 13. (c) 14. (d)
223 © John Bird Published by Taylor and Francis
