A bus that is traveling at 31.0 km/h, speeds up at a constant rate of 3.7 m/s2. What velocity does it reach 6.8 s later?

To find the final velocity of the bus, we can use the equation of motion:

vf = vi + at

where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time.

Given:
Initial velocity (vi) = 31.0 km/h = 31.0 x (1000/3600) m/s = 8.61 m/s
Acceleration (a) = 3.7 m/s^2
Time (t) = 6.8 s

Now we can substitute the values into the equation:

vf = 8.61 m/s + (3.7 m/s^2)(6.8 s)

vf = 8.61 m/s + 25.16 m/s

vf = 33.77 m/s

Therefore, the bus reaches a velocity of 33.77 m/s 6.8 seconds later.