Answer:
To find the distance the bus travels while braking, we need to determine the time it takes for the bus to come to a complete stop.
The bus is initially moving at 20 m/s, and it slows down at a rate of 4 m/s each second. We can calculate the time it takes for the bus to come to a stop using the formula:
t = (v_f - v_i) / a
where:
t is the time taken to stop,
v_f is the final velocity (0 m/s in this case, since the bus comes to a stop),
v_i is the initial velocity (20 m/s),
a is the acceleration (-4 m/s^2, since the bus is slowing down).
Plugging in the values:
t = (0 - 20) / (-4)
t = 20 / 4
t = 5 seconds
So, it takes 5 seconds for the bus to come to a complete stop.
To find the distance traveled, we use the formula:
d = v_i * t + 0.5 * a * t^2
where:
d is the distance traveled,
v_i is the initial velocity (20 m/s),
t is the time taken to stop (5 seconds),
a is the acceleration (-4 m/s^2).
Plugging in the values:
d = 20 * 5 + 0.5 * (-4) * 5^2
d = 100 + 0.5 * (-4) * 25
d = 100 + (-2) * 25
d = 100 - 50
d = 50 meters
Therefore, the bus travels a distance of 50 meters while braking.