9. A person walks fist at a constant speed of 6 km/h along a straight line from point A to point
B and then back along the same line from point B to A at a constant speed of 5 km/h for 2
hours. a) What is his total distance and displacement over the entire trip?
b) Find the total time taken for the entire trip.
c) Compute the average speed and average velocity of the person over the entire trip.
a) The total distance traveled is the sum of the distances traveled in each direction. Since the person walks at a constant speed of 6 km/h for the first leg of the trip, the distance traveled from A to B is given by
Distance_AB = Speed_AB * Time_AB
= 6 km/h * Time_AB
Similarly, the distance traveled from B to A is given by
Distance_BA = Speed_BA * Time_BA
= 5 km/h * Time_BA
The total distance traveled is the sum of these distances:
Total Distance = Distance_AB + Distance_BA
= 6 km/h * Time_AB + 5 km/h * Time_BA
b) The total time taken for the entire trip can be calculated by adding the times for each leg of the trip.
Total Time = Time_AB + Time_BA + Additional Time
We are given that the additional time, Time_BA, is 2 hours. To find the values of Time_AB and Time_BA in terms of the distance and speeds, we can use the formulas:
Time = Distance / Speed
Time_AB = Distance_AB / Speed_AB
= (6 km/h * Time_AB) / 6 km/h
= Time_AB
Time_BA = Distance_BA / Speed_BA
= (5 km/h * 2 hours) / 5 km/h
= 2 hours
Substituting these values into the total time equation:
Total Time = Time_AB + Time_BA + Additional Time
= Time_AB + 2 hours + 2 hours
= Time_AB + 4 hours
Therefore, the total time taken for the entire trip is Time_AB + 4 hours.
c) The average speed is given by the total distance divided by the total time:
Average Speed = Total Distance / Total Time
From part a), we know that the total distance is 6 km/h * Time_AB + 5 km/h * 2 hours. Substituting this and the expression for the total time from part b) into the average speed equation:
Average Speed = (6 km/h * Time_AB + 5 km/h * 2 hours) / (Time_AB + 4 hours)
The average velocity is the displacement divided by the total time taken. The displacement is the difference between the initial and final positions, which is zero since the person ends up back at point A. Therefore, the average velocity is also zero.
Average Velocity = 0 km/h.