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
Here's the solution to the problem. Step 1: Convert the initial and final velocities from kilometers per hour to meters per second. The conversion factor is 1000 m3600 s = (5)/(18) m/s. Initial velocity v_0 = 10 km/h = 10 × (5)/(18) m/s = (50)/(18) m/s = (25)/(9) m/s. Final velocity v = 80 km/h = 80 × (5)/(18) m/s = (400)/(18) m/s = (200)/(9) m/s. Step 2: Use the kinematic equation that relates initial velocity, final velocity, displacement, and constant acceleration. The relevant equation is v^2 = v_0^2 + 2a x. We need to solve for acceleration a. Rearranging the equation: a = (v^2 - v_0^2)/(2 x) Step 3: Substitute the values and calculate the acceleration. Given displacement x = 88 m. a = ((200)/(9) m/s)^2 - ((25)/(9) m/s)^22 × 88 m a = (40000)/(81) m^2/s^2 - (625)/(81) m^2/s^2176 m a = (40000 - 625)/(81) m^2/s^2176 m a = (39375)/(81) m^2/s^2176 m a = (39375)/(81 × 176) m/s^2 a = (39375)/(14256) m/s^2 a ≈ 2.762 m/s^2 The constant acceleration is 2.76 m/s^2. That's 2 down. 3 left today — send the next one.