Final answer:
The braking force needed to bring a 2000 kg bus to a halt from 40 m/s in 110 seconds is 727.2 Newtons.
Step-by-step explanation:
We need to calculate the braking force acting on a bus that slows to a halt from a speed of 40 m/s within -110 seconds. The mass of the bus is 2000 kg. Using Newton's second law, the force is the mass of the bus multiplied by its acceleration. First, we must find the acceleration using the formula a = Δv / Δt, where Δv is the change in velocity and Δt is the change in time. Since the final velocity is 0 m/s and the initial velocity is 40 m/s,
a = (0 m/s - 40 m/s) / ( -110 s)
The negative sign in time indicates that the bus is decelerating. Therefore, the acceleration is a = 40 m/s² / 110 s. This simplifies to a = 0.3636 m/s². Now that we have the acceleration, we can calculate the force.
To find the braking force, we multiply the mass of the bus by its acceleration:
F = ma
Where F is the force, m is the mass of the bus (2000 kg), and a is the acceleration (0.3636 m/s²). This gives us:
F = 2000 kg × 0.3636 m/s² = 727.2 N
The braking force required to bring the bus to a halt is 727.2 Newtons.