Final answer:
To calculate the time required for the truck to stop and the magnitude of the braking force, kinematic equations and Newton's second law are applied. First, the acceleration is determined using the stopping distance and initial speed, and then the time and braking force are calculated from this acceleration.
Step-by-step explanation:
To determine how long it takes for the truck to stop and the magnitude of the constant braking force acting on it, we need to use the concepts of kinematics and Newton's second law of motion.
Time Required to Stop
We can use the formula for acceleration, which is a = Δv / Δt, rearranged to solve for time (Δt): Δt = Δv / a. Since the final velocity (vf) is 0 m/s (because the truck stops) and the initial velocity (vi) is 25.0 m/s, and knowing that the truck travels 48.0 m before coming to a stop, we can first find the acceleration using the kinematic equation vf2 = vi2 + 2aΔx, and then find the time.
Braking Force
To find the braking force, we will use Newton's second law, F = ma, where F is the force, m is the mass of the truck, and a is the acceleration we previously calculated.