A bus that is traveling at 30.0 km/h speeds up at a constant rate of 3.5 m/s^2. what velocity does it reach 6.8 seconds later?
To determine the final velocity of the bus 6.8 seconds later, we can use the equation of motion:
final velocity (v) = initial velocity (u) + acceleration (a) * time (t)
First, let's convert the initial velocity from km/h to m/s:
Initial velocity (u) = 30.0 km/h
Since 1 km/h = 1000/3600 m/s, we can convert this as:
Initial velocity (u) = 30.0 * (1000/3600) m/s
= 8.33 m/s (rounded to two decimal places)
Next, the acceleration is given as 3.5 m/s^2, and the time is 6.8 seconds.
Using the equation of motion, we can calculate the final velocity:
v = u + a * t
= 8.33 m/s + (3.5 m/s^2) * (6.8 s)
= 8.33 m/s + 23.8 m/s
= 32.13 m/s (rounded to two decimal places)
Therefore, the bus reaches a velocity of 32.13 m/s (rounded to two decimal places) 6.8 seconds later.