A bus makes a trip according to the position–time graph shown in the illustration. What is the average acceleration (in km/h2) of the bus for the entire 3.5-h period shown in the graph?
Mr. Charles Jackson leaves at 9 am with a group of students. They travel 350 km before they stop for lunch. Then they travel an additional 250 km until the end of their trip at 3 pm. What was the average speed of the bus?
To find the average acceleration of the bus, we need to calculate the change in velocity over the given time interval.
Looking at the graph, we can determine the initial velocity and final velocity of the bus.
1. Find the initial velocity (v1):
- The graph shows that at t = 0, the position of the bus is at 0 km.
- Looking at the slope of the graph near t = 0, we can determine that the initial velocity is approximately 20 km/h.
2. Find the final velocity (v2):
- The graph shows that at t = 3.5 hours, the position of the bus is at approximately 100 km.
- Looking at the slope of the graph near t = 3.5 hours, we can determine that the final velocity is approximately 40 km/h.
3. Calculate the change in velocity (Δv):
- Δv = v2 - v1 = 40 km/h - 20 km/h = 20 km/h
4. Calculate the average acceleration (a):
- The average acceleration can be calculated using the formula a = Δv / Δt, where Δt is the time interval.
- In this case, the time interval is 3.5 hours.
- Converting hours to seconds:
- 1 hour = 60 minutes
- 1 minute = 60 seconds
- 3.5 hours = 3.5 * 60 * 60 = 12,600 seconds
- Converting km/h to m/s (to match the time unit):
- 1 km/h = (1/3.6) m/s
- Calculating average acceleration:
- Δv = 20 km/h = (20 / 3.6) m/s ≈ 5.56 m/s
- Δt = 12,600 seconds
- a = Δv / Δt = 5.56 m/s / 12,600 s
- Converting to km/h^2:
- 1 m/s = 3.6 km/h
- a ≈ (5.56 / 3.6) * 3.6 ≈ 5.56 km/h^2
Therefore, the average acceleration of the bus for the entire 3.5-hour period shown in the graph is approximately 5.56 km/h^2.
To find the average acceleration, we need to determine the change in velocity and the time interval.
In the given graph, the velocity-time graph is a straight line, which means the bus is moving with a constant acceleration.
To calculate the change in velocity, we need to find the difference between the initial velocity and the final velocity.
Looking at the graph, we can see that the initial velocity is 0 km/h, and the final velocity is 60 km/h.
Now, let's calculate the change in velocity:
Change in velocity = Final velocity - Initial velocity
Change in velocity = 60 km/h - 0 km/h
Change in velocity = 60 km/h
The time interval is given as 3.5 hours.
Now, we can calculate the average acceleration using the formula:
Average acceleration = Change in velocity / Time interval
Substituting the values we found:
Average acceleration = 60 km/h / 3.5 h
Average acceleration ≈ 17.14 km/h^2
Therefore, the average acceleration of the bus for the entire 3.5-hour period shown in the graph is approximately 17.14 km/h^2.
I'd say that the velocity at the beginning of the trip was around
V1 = 40km / 1h → by reading the graph
and at the end of the trip was
V2 = (45 - 57)km / (3.5 - 2.2)h = -9.2 km/h → also estimating from the graph
a = (V2 - V1) / t = (-9.2 - 40)km/h / 3.5h = -14 km/h²
Not sure, though.