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.