The problem involves calculating the acceleration of a bus that slows down from an initial speed to a lower speed over a specific time frame. Let’s break this down step by step.
1. **Identify Initial and Final Velocities**:
The initial speed (u) of the bus is 80 kilometers per hour (km/h), and the final speed (v) is 60 kilometers per hour.
2. **Convert the Speeds to Meters per Second**:
Since acceleration is measured in meters per second squared (m/s²), we must convert the speeds from km/h to m/s.
– To convert km/h to m/s, we use the conversion factor: 1 km/h = 1/3.6 m/s.
– Therefore:
– Initial speed (u) = 80 km/h = 80 / 3.6 ≈ 22.22 m/s
– Final speed (v) = 60 km/h = 60 / 3.6 ≈ 16.67 m/s
3. **Use the Formula for Acceleration**:
Acceleration (a) is defined as the change in velocity divided by the time taken for that change. The formula is:
a = (v – u) / t
where:
– v = final velocity
– u = initial velocity
– t = time (in seconds)
4. **Substituting the Values**:
Now, we substitute the known values into the formula:
– Change in velocity (v – u) = 16.67 m/s – 22.22 m/s = -5.55 m/s
– Time (t) = 5 seconds
Thus, the equation becomes:
a = (-5.55 m/s) / (5 s)
5. **Calculating Acceleration**:
When we perform the calculation:
a = -1.11 m/s²
6. **Interpret the Result**:
The negative sign indicates that the bus is decelerating (slowing down), with an acceleration of approximately -1.11 meters per second squared.
In conclusion, the acceleration of the bus as it decreases its speed from 80 km/h to 60 km/h in 5 seconds is approximately -1.11 m/s².