Example 4 A man walks on a straight road from his home to a market 3 km away with a
speed of 6 km/h finding the market closed, he instantly turns and walks back with a speed of 9 km/h.
What is the (a) magnitude of average velocity and (b) average speed of the man, over the interval of
time (i) 0 to 30 min, (ii) 0 to 50 min, (iii) 0 to 40 min?
Answers
Answer:
Distance to market s=2.5km=2.5×10
3
=2500m
Speed with which he goes to market =5km/h=5
3600
10
3
=
18
25
m/s
Speed with which he comes back =7.5km/h=7.5×
3600
10
3
=
36
75
m/s
(a)Average velocity is zero since his displacement is zero.
(b)
(i)Since the initial speed is 5km/s and the market is 2.5 km away,time taken to reach market:
5
2.5
=1/2h=30 minutes.
Average speed over this interval =5km/h
(ii)After 30 minutes,the man is travelling wuth 7.5 km/h speed for 50-30=20 minutes.The distance he covers in 20 minutes :7.5×
3
1
=2.5km
His average speed in 0 to 50 minutes: V
avg
=
time
distancetraveled
=
(50/60)
2.5+2.5
=6km/h
(iii)In 40-30=10 minutes he travels a distance of :7.5×
6
1
=1.25km
V
avg
=
(40/60)
2.5+1.25
=5.625km/h
Answer:
Average speed from home to market: 6 kmph
time taken from home to market: 3 km/ 6 kmph = 1/2 hr = 30 min
So this is the average speed for 0 to 30 min.: 6 kmph
Average speed from market to home 9 kmph Time taken from market to home on the way back: 3 km/9kmph = 1/3 hour
Average speed for the total journey: from to market and market to home :
= total distance / total time = (3 km +3 km )/[ 1/2 +1/3 Jhr
= 6/(5/6) = 36/5 = 7.2 kmph
This is average speed for 0 to 50 min
distance traveled from 30 to 40 minutes, that
is 10 min: 1/6 hr
= 9 kmph * 1/6 hour = 1.5 km
Average speed for time =0 to 40 min is = distance traveled / time taken = (3 +
1.5) / (40/60)
= 4.5 * 60 / 40 = 6.75 kmph
Velocity = change in displacement vector = vector joining initial position of man and
final position of man
Velocity is dependent on the current position of man and not the distance traveled by man.
Velocity initially at t=0 is 0, as the man is at
home.
Velocity for t = 0 to 30 minutes is : 6 kmph towards the market.
Velocity at t = 50 minutes is zero as the man is at home. THat is, displacement of the man from initial position is zero. So displacement/time = 0.
Distance of the man from home at t = 40 min is : 3 - 1.5 km = 1.5 km Velocity at time 40 minutes is: 1.5 km/(40/60)
hr = 2.25 kmph
The direction of velocity is in the direction towards market from home.