This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Welcome back omahendrea@gmail.com — been a while! Let's pick up where you left off. Here's how to determine if the bus will stop in time: Step 1: Convert the initial velocity to meters per second. The initial velocity u = 36 km h^-1. u = 36 km h^-1 × 1000 m1 km × 1 h3600 s = 10 m s^-1 Step 2: Calculate the distance covered during the reaction time. The driver takes 0.5 s to react. d_reaction = u × t_reaction d_reaction = 10 m s^-1 × 0.5 s = 5 m Step 3: Calculate the distance covered while braking. The initial velocity for braking is u = 10 m s^-1, the final velocity v = 0 m s^-1 (since the bus stops), and the acceleration a = -2.5 m s^-2 (negative because it's deceleration). Using the kinematic equation v^2 = u^2 + 2as: 0^2 = (10 m s^-1)^2 + 2(-2.5 m s^-2)s_braking 0 = 100 m^2 s^-2 - 5 m s^-2 · s_braking 5 m s^-2 · s_braking = 100 m^2 s^-2 s_braking = 100 m^2 s^-25 m s^-2 = 20 m Step 4: Calculate the total stopping distance. The total stopping distance is the sum of the reaction distance and the braking distance. D_total = d_reaction + s_braking D_total = 5 m + 20 m = 25 m Step 5: Compare the total stopping distance with the obstacle distance. The obstacle is 30 m ahead. Since 25 m < 30 m, the bus will stop before reaching the obstacle. The bus will be able to stop before reaching the obstacle. The total stopping distance is 25 m. Send me the next one 📸