A bus slows down uniformly from 79.6 km/h (22.1 m/s) to 0 km/h in 15 s. How far does it travel before stopping?
To find the distance the bus travels before stopping, we can use the formula:
distance = (initial velocity × time) + (0.5 × acceleration × time²)
In this case, the initial velocity is 22.1 m/s (which is the same as 79.6 km/h), the final velocity is 0 m/s, and the time is 15 seconds. We need to find the acceleration to solve the problem.
Acceleration can be calculated using the equation:
acceleration = (final velocity - initial velocity) / time
Plugging in the given values, we have:
acceleration = (0 - 22.1) m/s / 15 s
acceleration = -1.47333 m/s²
Now we can plug this acceleration value into the distance formula:
distance = (22.1 m/s × 15 s) + (0.5 × -1.47333 m/s² × (15 s)²)
distance = 331.5 m - 1106.67 m
distance = -775.17 m
The negative distance indicates that the bus moves in the opposite direction. Therefore, the bus travels 775.17 meters before coming to a stop.