Final answer:
a. The bus's acceleration during the time interval is -5.45 m/s². b. The negative sign of the acceleration indicates that the bus is decelerating. c. The bus does not hit the pedestrian as it comes to a halt before reaching them.
Step-by-step explanation:
a. To find the bus's acceleration, we can use the formula acceleration (a) = change in velocity (Δv) / time taken (Δt). In this case, the initial velocity (u) of the bus is 9.0 m/s and the final velocity (v) is 0 m/s since it comes to a halt. Therefore, the change in velocity (Δv) = v - u = 0 - 9.0 = -9.0 m/s. The time taken (Δt) is given as 1.65 s. Plugging these values into the formula, we get:Acceleration (a) = -9.0 m/s / 1.65 s = -5.45 m/s²
Therefore, the bus's acceleration during this time interval is -5.45 m/s².
b. The negative sign of the acceleration indicates that the bus is decelerating or slowing down.
c. To determine if the bus hits the pedestrian, we need to calculate the distance it takes for the bus to come to a halt. We can use the formula v² = u² + 2aΔx, where v is the final velocity (0 m/s), u is the initial velocity (9.0 m/s), a is the acceleration (-5.45 m/s²), and Δx is the distance traveled by the bus. Plugging in these values, we get:
0² = 9.0² + 2(-5.45)Δx
Simplifying, we get:
-109.35Δx = -81.0
Δx = -81.0 / -109.35
Δx = 0.74 m
Since the pedestrian is 10 m away from the bus, which is greater than the distance it takes for the bus to come to a halt (0.74 m), it means the bus does not hit the pedestrian.