A man walks on a straight road from his home to a market 2.5 km away with a speed of 5 km h⁻¹. Finding the market closed, instantly turns and walks back home with a speed of 7.5 km h⁻¹. What is thea. the magnitude of average velocity andb. average speed of the man over the interval of time (i) 0 to 30 min (ii) 0 to 50 min and (iii) 0 to 40 minutes
Answers
# Answers-
Time taken by the man to reach the market from home,
t1 = 2.5/5 = 1/2 h = 30 min
Time taken by the man to reach home from the market,
t2 = 2.5/7.5 = 1/3 h = 20 min
Total time taken in the whole journey = 30 + 20 = 50 min
# Formula-
1. Magnitude of average velocity = displacement/time
2. Average speed = total distance travelled/time
# Calculations-
(i) 0 to 30 min-
Average velocity = 2.5/0.5 = 5 km/h
Average speed = 2.5/0.5 = 5 km/h
(ii) 0 to 50 min
Average velocity = 0/0.83 = 0
Average speed = 5/0.83 = 6 km/h
(iii) 0 to 40 min
Average velocity = 1.25/0.66 = 1.875 km/h
Average speed = 3.75/0.66 = 5.625 km/h
Hope you got your answer...
Given:
Distance of the man from his home to the market = 2.5 kilometre
Speed of the man while walking to the market from his home = 5 km h^-1
The speed at whihc he instantly turns back and walks back to his house = 7.5 km h^-1
The Formula used to calculate speed
= distance / time
So time will be
Distance / Speed
Now calculating time taken by the man to reach the market by using the above formula:
t = S/v
Substituting the values known to us in the formula we get:
t = 2.5 / 5
t = 0.5 hours
Calculating the time taken by the man to reach back to his house:
t1 = S/v1
Substituting the values known to us in the formula we get:
t1 = 2.5 / 7.5
t1 = 0.333 hours
(i) Calculating average velocity for (0 - 30 mins)
= Delta x / Delta t
Substituting the values into this formula we get:
= 2.5 / 0.5 (In 0.5 hrs the distance covered by the man is 2.5 km)
= 5 km h^-1
(ii) Calculating average velocity for the time period 0 to 50 mins
= (2.5 + 2.5) km / (0.5 + 0.333)
= (5) / 0.8333
= 6 km h^-1
(iii) Calculating average velocity for the time period 0 to 40 mins:
= Delta X / Delta T
= (2.5 + 2.5/2) / 40/60
(Because during the first 30 mins distance covered is 2.5 so by knowing this the distance covered in the next 10 mins is 2.5/2 kilometres in the return journey)
= 5.625 km h^-1