Calculating Time for Mate to Catch up with Bus
Calculation:
Given data:
Uniform acceleration of the bus: 2m/s2
Starting position of the mate behind the bus: 9m
Uniform speed of the mate: 6m/s
Let's denote the position of the bus as xbus at time t:
xbus = (1/2) * (2m/s2) * t2
If we take the bus's rear's starting position to be the origin, then the position of the mate, xmate, is:
xmate = -9m + (6m/s) * t
The mate catches up with the bus when xbus = xmate:
(1/2) * (2m/s2) * t2 = -9m + (6m/s) * t
Simplifying the equation:
2t2 = -9 + 6t
t2 - 6t + 9 = (t - 3)2 = 0
Therefore, t = 3 seconds
Thus, the mate will take 3 seconds to catch up with the bus.