Starting from home, you bicycle 22km north in 2.3h and then turn around and pedal straight home in 1.3h . What are your (a) displacement at the end of the first 2.3h , (b) average velocity over the first 2.3h , (c) average velocity for the homeward leg of the trip, (d) displacement for the entire trip, and (e) average velocity for the entire trip?
To find the answers to these questions, we'll break down each part step by step:
(a) Displacement at the end of the first 2.3h:
Displacement refers to the change in position from the starting point to the ending point. Since you are traveling north and then turning around to return home, the displacement at the end of the first 2.3 hours would simply be the distance traveled towards the north.
In this case, you traveled 22 km north, so the displacement at the end of the first 2.3 hours is 22 km north.
(b) Average velocity over the first 2.3h:
Average velocity is calculated by dividing the total displacement by the total time taken. In this case, the total displacement is 22 km north, and the total time taken is 2.3 hours.
So, to find the average velocity, you divide the displacement (22 km north) by the time (2.3 hours). This gives us an average velocity of (22 km north) / (2.3 hours), which is approximately 9.57 km/h north.
(c) Average velocity for the homeward leg of the trip:
Since you pedal straight home in 1.3 hours, the displacement for this leg of the trip is 0 km since you returned to your starting point. Therefore, the average velocity for the homeward leg of the trip is (0 km) / (1.3 hours), which is 0 km/h.
(d) Displacement for the entire trip:
The displacement for the entire trip is the sum of the displacements for each leg of the trip. In the first leg, you traveled 22 km north, and in the homeward leg, you traveled 0 km. Therefore, the total displacement for the entire trip is 22 km north + 0 km = 22 km north.
(e) Average velocity for the entire trip:
The average velocity for the entire trip is calculated by dividing the total displacement by the total time taken. In this case, the total displacement is 22 km north, and the total time taken is the sum of the times for both legs of the trip (2.3 hours + 1.3 hours).
So, to find the average velocity, you divide the displacement (22 km north) by the time (2.3 hours + 1.3 hours). This gives us an average velocity of (22 km north) / (3.6 hours), which is approximately 6.11 km/h north.