To find the rate at which the velocity of the bus changes, we need to calculate the acceleration. The formula to calculate acceleration is:
acceleration (a) = (final velocity (v) - initial velocity (u)) / time (t)
Given: Initial velocity (u) = 0 (since the bus is initially at rest) Final velocity (v) = 80 km/h = 80 * (1000 m / 3600 s) = 800/9 m/s (converting km/h to m/s) Time (t) = 20 s
Substituting the values into the formula:
a = (800/9 m/s - 0) / 20 s
Simplifying:
a = (800/9 m/s) / 20 s a = 40/9 m/s²
Therefore, the acceleration of the bus is 40/9 m/s².
Now, to find the rate at which the velocity changes, we take the derivative of velocity with respect to time. Since acceleration is the derivative of velocity with respect to time, the rate at which the velocity changes is equal to the acceleration.
Thus, the rate at which the velocity of the bus changes is 40/9 m/s².