- Calculating Acceleration of the Bus
To calculate the acceleration of the bus, we can use the formula:
\[ \text{Acceleration} = \frac{\text{Change in Velocity}}{\text{Time Taken}} \]
- Given Data
Initial velocity, \( u = 90 \, \text{km/h} \)
Final velocity, \( v = 72 \, \text{km/h} \)
Time taken, \( t = 5 \, \text{seconds} \)
- Converting Velocities to m/s
To calculate acceleration, we need to convert the velocities from km/h to m/s. We can do this by using the conversion factor 1 km/h = 0.2778 m/s.
Initial velocity in m/s: \( 90 \times 0.2778 = 25 \, \text{m/s} \)
Final velocity in m/s: \( 72 \times 0.2778 = 20 \, \text{m/s} \)
- Calculating Change in Velocity
Change in velocity = Final velocity - Initial velocity
Change in velocity = \( 20 \, \text{m/s} - 25 \, \text{m/s} = -5 \, \text{m/s} \)
- Calculating Acceleration
Acceleration = Change in velocity / Time taken
Acceleration = \( \frac{-5 \, \text{m/s}}{5 \, \text{seconds}} = -1 \, \text{m/s}^2 \)
Therefore, the acceleration of the bus is \( -1 \, \text{m/s}^2 \). The negative sign indicates that the bus is decelerating, or slowing down.